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  journal       = {arXiv e-prints},
  keywords      = {Mathematics - Combinatorics, 05E05, 06A11},
  year          = 2022,
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  primaryclass  = {math.CO},
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}


@misc{A-KE,
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@misc{ArdilaSanchez,
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@article{bjorner-ziegler,
  author     = {Bj\"{o}rner, Anders and Ziegler, G\"{u}nter M.},
  doi        = {10.1016/0095-8956(91)90008-8},
  fjournal   = {Journal of Combinatorial Theory. Series B},
  issn       = {0095-8956},
  journal    = {J. Combin. Theory Ser. B},
  mrclass    = {52B40 (05B35)},
  mrnumber   = {1088629},
  mrreviewer = {Michel Yves Jambu},
  number     = {1},
  pages      = {96--126},
  title      = {Broken {C}ircuit {C}omplexes: {F}actorizations and {G}eneralizations},
  url        = {https://doi.org/10.1016/0095-8956(91)90008-8},
  volume     = {51},
  year       = {1991},
  bdsk-url-1 = {https://doi.org/10.1016/0095-8956(91)90008-8}
}

@book{BjornerEtAl,
  author     = {Bj\"{o}rner, Anders and Las Vergnas, Michel and Sturmfels, Bernd and White, Neil and Ziegler, G\"{u}nter M.},
  doi        = {10.1017/CBO9780511586507},
  edition    = {Second},
  isbn       = {0-521-77750-X},
  mrclass    = {52B40 (05B35 52C35)},
  mrnumber   = {1744046},
  pages      = {xii+548},
  publisher  = {Cambridge University Press},
  series     = {Encyclopedia of Mathematics and its Applications, Volume 46},
  title      = {Oriented {M}atroids},
  url        = {https://doi.org/10.1017/CBO9780511586507},
  year       = {1999},
  bdsk-url-1 = {https://doi.org/10.1017/CBO9780511586507}
}

@article{BjornerWachs1,
  author     = {Bj\"{o}rner, Anders and Wachs, Michelle L.},
  doi        = {10.2307/2000946},
  fjournal   = {Transactions of the American Mathematical Society},
  issn       = {0002-9947},
  journal    = {Trans. Amer. Math. Soc.},
  mrclass    = {05A99 (06F99 20B30 20F99)},
  mrnumber   = {946427},
  mrreviewer = {Joseph Kung},
  number     = {1},
  pages      = {1--37},
  title      = {Generalized {Q}uotients in {C}oxeter {G}roups},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.2307/2000946},
  volume     = {308},
  year       = {1988},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.2307/2000946},
  bdsk-url-2 = {https://doi.org/10.2307/2000946}
}

@article{BjornerWachs2,
  author     = {Bj\"{o}rner, Anders and Wachs, Michelle L.},
  doi        = {10.1016/0097-3165(89)90028-9},
  fjournal   = {Journal of Combinatorial Theory. Series A},
  issn       = {0097-3165},
  journal    = {J. Combin. Theory Ser. A},
  mrclass    = {05A30 (05A15 05E25)},
  mrnumber   = {1022316},
  number     = {2},
  pages      = {165--187},
  title      = {{$q$}-hook {L}ength {F}ormulas for {F}orests},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.1016/0097-3165(89)90028-9},
  volume     = {52},
  year       = {1989},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.1016/0097-3165(89)90028-9},
  bdsk-url-2 = {https://doi.org/10.1016/0097-3165(89)90028-9}
}

@article{BjornerWachs3,
  author     = {Bj\"{o}rner, Anders and Wachs, Michelle L.},
  doi        = {10.1016/0097-3165(91)90075-R},
  fjournal   = {Journal of Combinatorial Theory. Series A},
  issn       = {0097-3165},
  journal    = {J. Combin. Theory Ser. A},
  mrclass    = {06A07 (05E99 20B35)},
  mrnumber   = {1119703},
  mrreviewer = {Sergey V. Fomin},
  number     = {1},
  pages      = {85--114},
  title      = {Permutation {S}tatistics and {L}inear {E}xtensions of {P}osets},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.1016/0097-3165(91)90075-R},
  volume     = {58},
  year       = {1991},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.1016/0097-3165(91)90075-R},
  bdsk-url-2 = {https://doi.org/10.1016/0097-3165(91)90075-R}
}

@article{BjornerWachs4,
  author     = {Bj\"{o}rner, Anders and Wachs, Michelle L.},
  doi        = {10.1090/S0002-9947-96-01534-6},
  fjournal   = {Transactions of the American Mathematical Society},
  issn       = {0002-9947},
  journal    = {Trans. Amer. Math. Soc.},
  mrclass    = {06A08 (05E99 52B99)},
  mrnumber   = {1333388},
  mrreviewer = {T. S. Blyth},
  number     = {4},
  pages      = {1299--1327},
  title      = {Shellable {N}onpure {C}omplexes and {P}osets. {I}},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.1090/S0002-9947-96-01534-6},
  volume     = {348},
  year       = {1996},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.1090/S0002-9947-96-01534-6},
  bdsk-url-2 = {https://doi.org/10.1090/S0002-9947-96-01534-6}
}

@article{bland-lasvergnas,
  author     = {Bland, Robert G. and Las Vergnas, Michel},
  doi        = {10.1016/0095-8956(78)90080-1},
  fjournal   = {Journal of Combinatorial Theory. Series B},
  issn       = {0095-8956},
  journal    = {J. Combinatorial Theory Ser. B},
  mrclass    = {05B35},
  mrnumber   = {485461},
  mrreviewer = {Thomas Brylawski},
  number     = {1},
  pages      = {94--123},
  title      = {Orientability of {M}atroids},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.1016/0095-8956(78)90080-1},
  volume     = {24},
  year       = {1978},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.1016/0095-8956(78)90080-1},
  bdsk-url-2 = {https://doi.org/10.1016/0095-8956(78)90080-1}
}

@article{branden,
  author     = {Br\"{a}nd\'{e}n, Petter},
  doi        = {10.1016/j.disc.2003.07.006},
  fjournal   = {Discrete Mathematics},
  issn       = {0012-365X},
  journal    = {Discrete Math.},
  mrclass    = {06A07 (05A10 05E10 05E25)},
  mrnumber   = {2047757},
  mrreviewer = {Edward B. Swartz},
  number     = {1-3},
  pages      = {67--81},
  title      = {{$q$}-{N}arayana {N}umbers and the {F}lag {$h$}-vector of {$J(\bold 2\times\bold n)$}},
  url        = {https://doi-org.ezp3.lib.umn.edu/10.1016/j.disc.2003.07.006},
  volume     = {281},
  year       = {2004},
  bdsk-url-1 = {https://doi-org.ezp3.lib.umn.edu/10.1016/j.disc.2003.07.006},
  bdsk-url-2 = {https://doi.org/10.1016/j.disc.2003.07.006}
}

@article{brenti-welker,
  abstract      = {For a simplicial complex or more generally Boolean cell complex Δwe study the behavior of the f- and h-vector under barycentric subdivision. We show that if Δhas a non-negative h-vector then the h-polynomial of its barycentric subdivision has only simple and real zeros. As a consequence this implies a strong version of the Charney--Davis conjecture for spheres that are the subdivision of a Boolean cell complex or the subdivision of the boundary complex of a simple polytope. For a general (d −1)-dimensional simplicial complex Δthe h-polynomial of its n-th iterated subdivision shows convergent behavior. More precisely, we show that among the zeros of this h-polynomial there is one converging to infinity and the other d −1 converge to a set of d −1 real numbers which only depends on d.},
  author        = {Brenti, Francesco and Welker, Volkmar},
  date          = {2008/08/01},
  date-added    = {2022-09-29 04:54:33 -0500},
  date-modified = {2022-09-29 04:54:33 -0500},
  doi           = {10.1007/s00209-007-0251-z},
  id            = {Brenti2008},
  isbn          = {1432-1823},
  journal       = {Mathematische Zeitschrift},
  number        = {4},
  pages         = {849--865},
  title         = {f-Vectors of barycentric subdivisions},
  url           = {https://doi.org/10.1007/s00209-007-0251-z},
  volume        = {259},
  year          = {2008},
  bdsk-url-1    = {https://doi.org/10.1007/s00209-007-0251-z}
}

@article{Brown,
  author     = {Brown, Kenneth S.},
  doi        = {10.1023/A:1007822931408},
  fjournal   = {Journal of Theoretical Probability},
  issn       = {0894-9840},
  journal    = {J. Theoret. Probab.},
  mrclass    = {60J10 (20M99 60B15)},
  mrnumber   = {1785534},
  number     = {3},
  pages      = {871--938},
  title      = {Semigroups, {R}ings, and {M}arkov {C}hains},
  url        = {https://doi.org/10.1023/A:1007822931408},
  volume     = {13},
  year       = {2000},
  bdsk-url-1 = {https://doi.org/10.1023/A:1007822931408}
}

@article{Budur-Nero-Mustata,
  author     = {Budur, Nero and Musta\c{t}\u{a}, Mircea and Teitler, Zach},
  title      = {The monodromy conjecture for hyperplane arrangements},
  journal    = {Geom. Dedicata},
  fjournal   = {Geometriae Dedicata},
  volume     = {153},
  year       = {2011},
  pages      = {131--137},
  issn       = {0046-5755,1572-9168},
  mrclass    = {32S40 (32S22)},
  mrnumber   = {2819667},
  mrreviewer = {Uli\ Walther},
  doi        = {10.1007/s10711-010-9560-1},
  url        = {https://doi.org/10.1007/s10711-010-9560-1}
}

@incollection{cellinipapi,
  author     = {Cellini, Paola and Papi, Paolo},
  doi        = {10.1016/S0021-8693(02)00532-X},
  fjournal   = {Journal of Algebra},
  issn       = {0021-8693},
  journal    = {J. Algebra},
  mrclass    = {17B20 (17B05 17B30)},
  mrnumber   = {1958899},
  mrreviewer = {Jorge A. Vargas},
  note       = {Special issue in celebration of Claudio Procesi's 60th birthday},
  number     = {1},
  pages      = {112--121},
  title      = {Ad-nilpotent ideals of a {B}orel subalgebra. {II}},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.1016/S0021-8693(02)00532-X},
  volume     = {258},
  year       = {2002},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.1016/S0021-8693(02)00532-X},
  bdsk-url-2 = {https://doi.org/10.1016/S0021-8693(02)00532-X}
}

@article{chapoton,
  author  = {Chapoton, Fr\'{e}d\'{e}ric},
  journal = {arXiv 0303220},
  pages   = {1--7},
  title   = {Antichains of positive roots and {H}eaviside functions},
  year    = {2003}
}

@misc{Chapuy-Douvropoulos,
  author     = {Chapuy, Guillaume and Douvropoulos, Theo},
  copyright  = {arXiv.org perpetual, non-exclusive license},
  doi        = {10.48550/ARXIV.2012.04519},
  keywords   = {Combinatorics (math.CO), Representation Theory (math.RT), Spectral Theory (math.SP), FOS: Mathematics, FOS: Mathematics, 05E99 (Primary) 05A15, 05C05, 20C99, 20F55, 47A99 (Secondary)},
  publisher  = {arXiv},
  title      = {Coxeter factorizations with generalized Jucys-Murphy weights and Matrix Tree theorems for reflection groups},
  url        = {https://arxiv.org/abs/2012.04519},
  year       = {2020},
  bdsk-url-1 = {https://arxiv.org/abs/2012.04519},
  bdsk-url-2 = {https://doi.org/10.48550/ARXIV.2012.04519}
}

@article{conca,
  author     = {Conca, Aldo},
  doi        = {10.1006/aama.1999.0676},
  fjournal   = {Advances in Applied Mathematics},
  issn       = {0196-8858},
  journal    = {Adv. in Appl. Math.},
  mrclass    = {13P10 (14Q99 68W30)},
  mrnumber   = {1748965},
  mrreviewer = {Francisco Jes\'{u}s Castro-Jim\'{e}nez},
  number     = {2},
  pages      = {111--124},
  title      = {Gr\"{o}bner {B}ases for {S}paces of {Q}uadrics of {L}ow {C}odimension},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.1006/aama.1999.0676},
  volume     = {24},
  year       = {2000},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.1006/aama.1999.0676},
  bdsk-url-2 = {https://doi.org/10.1006/aama.1999.0676}
}

@article{Cordovil,
  author     = {Cordovil, R.},
  doi        = {10.1007/s00454-001-0053-8},
  fjournal   = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science},
  issn       = {0179-5376},
  journal    = {Discrete Comput. Geom.},
  mrclass    = {52C40 (05B35 52C35)},
  mrnumber   = {1871690},
  mrreviewer = {Laura M. Anderson},
  pages      = {73--84},
  publisher  = {Springer},
  title      = {A {C}ommutative {A}lgebra for {O}riented {M}atroids},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.1007/s00454-001-0053-8},
  volume     = {27},
  year       = {2002},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.1007/s00454-001-0053-8},
  bdsk-url-2 = {https://doi.org/10.1007/s00454-001-0053-8}
}

@book{cox-little-oshea,
  author     = {Cox, David A. and Little, John and O'Shea, Donal},
  doi        = {10.1007/978-3-319-16721-3},
  edition    = {Fourth},
  isbn       = {978-3-319-16720-6; 978-3-319-16721-3},
  mrclass    = {13P10 (13-01 14-01 14Qxx 68W30)},
  mrnumber   = {3330490},
  note       = {An introduction to computational algebraic geometry and commutative algebra},
  pages      = {xvi+646},
  publisher  = {Springer},
  series     = {Undergraduate Texts in Mathematics},
  title      = {Ideals, {V}arieties, and {A}lgorithms},
  url        = {https://doi-org.ezp3.lib.umn.edu/10.1007/978-3-319-16721-3},
  year       = {2015},
  bdsk-url-1 = {https://doi-org.ezp3.lib.umn.edu/10.1007/978-3-319-16721-3},
  bdsk-url-2 = {https://doi.org/10.1007/978-3-319-16721-3}
}

@article{coxeter,
  author     = {Coxeter, H.S.M},
  doi        = {https://doi.org/10.1112/jlms/s1-10.37.21},
  fjournal   = {J. London Math. Soc.},
  issn       = {0894-9840},
  journal    = {J. London Math. Soc.},
  number     = {1},
  pages      = {21-25},
  title      = {The complete enumeration of finite groups of the form {$R_i^2 = (R_i R_j)^{k_{ij}} = 1$}},
  url        = {https://doi.org/10.1112/jlms/s1-10.37.21},
  volume     = {10},
  year       = {1935},
  bdsk-url-1 = {https://doi.org/10.1112/jlms/s1-10.37.21}
}

@article{cuntz-stump,
  author     = {Cuntz, Michael and Stump, Christian},
  doi        = {10.1090/S0025-5718-2014-02841-X},
  fjournal   = {Mathematics of Computation},
  issn       = {0025-5718},
  journal    = {Math. Comp.},
  mrclass    = {17B22 (06A06 20F55)},
  mrnumber   = {3266972},
  mrreviewer = {Alan J. X. Guo},
  number     = {291},
  pages      = {485--503},
  title      = {On root posets for noncrystallographic root systems},
  url        = {https://doi.org/10.1090/S0025-5718-2014-02841-X},
  volume     = {84},
  year       = {2015},
  bdsk-url-1 = {https://doi.org/10.1090/S0025-5718-2014-02841-X}
}

@article{Davidson-Hersh,
  abstract   = {Geometric lattices are characterized in this paper as those finite, atomic lattices such that every atom ordering induces a lexicographic shelling given by an edge labeling known as a minimal labeling. Equivalently, geometric lattices are shown to be exactly those finite lattices such that every ordering on the join-irreducibles induces a lexicographic shelling. This new characterization fits into a similar paradigm as McNamaraʼs characterization of supersolvable lattices as those lattices admitting a different type of lexicographic shelling, namely one in which each maximal chain is labeled with a permutation of {1,{\ldots},n}.},
  author     = {Ruth Davidson and Patricia Hersh},
  doi        = {https://doi.org/10.1016/j.jcta.2013.11.001},
  issn       = {0097-3165},
  journal    = {Journal of Combinatorial Theory, Series A},
  keywords   = {Geometric lattice, M{\"o}bius function, Shellability, Order complex},
  number     = {1},
  pages      = {8-13},
  title      = {A lexicographic shellability characterization of geometric lattices},
  url        = {https://www.sciencedirect.com/science/article/pii/S0097316513001659},
  volume     = {123},
  year       = {2014},
  bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0097316513001659},
  bdsk-url-2 = {https://doi.org/10.1016/j.jcta.2013.11.001}
}

@misc{db-m-s,
  title         = {The Poincar\'e-extended ab-index},
  author        = {Galen Dorpalen-Barry and Joshua Maglione and Christian Stump},
  year          = {2023},
  eprint        = {2301.05904},
  archiveprefix = {arXiv},
  primaryclass  = {math.CO}
}

@article{delucchi,
  author   = {Delucchi, Emanuele},
  fjournal = {Thesis (Ph.D.)},
  journal  = {Thesis (Ph.D.)--Swiss Federal Institute of Technology},
  title    = {Combinatorics and {T}opology of {A}rrangement {C}overs and of {N}ested {S}et {C}omplexes},
  year     = {2006}
}

@incollection{Denef,
  author     = {Denef, Jan},
  title      = {Report on {I}gusa's local zeta function},
  note       = {S\'{e}minaire Bourbaki, Vol. 1990/91},
  journal    = {Ast\'{e}risque},
  fjournal   = {Ast\'{e}risque},
  number     = {201-203},
  year       = {1991},
  pages      = {Exp. No. 741, 359--386},
  issn       = {0303-1179,2492-5926},
  mrclass    = {11S40 (14G20)},
  mrnumber   = {1157848},
  mrreviewer = {Boris\ Datskovsky}
}

@article{denham,
  author        = {Graham Denham and Phil Hanlon},
  date-added    = {2019-02-08 10:31:52 -0600},
  date-modified = {2019-02-08 10:31:52 -0600},
  journal       = {Pacific Journal of Mathematics},
  number        = {3},
  pages         = {123-146},
  title         = {On the {S}mith {N}ormal Form of the {V}archenko {B}ilinear {F}orm of a {H}yperplane {A}rrangement},
  volume        = {181},
  year          = {1997}
}

@misc{DNP,
  author     = {Delucchi, Emanuele and Girard, Noriane and Paolini, Giovanni},
  copyright  = {arXiv.org perpetual, non-exclusive license},
  doi        = {10.48550/ARXIV.1706.06360},
  keywords   = {Combinatorics (math.CO), FOS: Mathematics, FOS: Mathematics},
  publisher  = {arXiv},
  title      = {Shellability of posets of labeled partitions and arrangements defined by root systems},
  url        = {https://arxiv.org/abs/1706.06360},
  year       = {2017},
  bdsk-url-1 = {https://arxiv.org/abs/1706.06360},
  bdsk-url-2 = {https://doi.org/10.48550/ARXIV.1706.06360}
}

@article{dorpalenbarry,
  author  = {Galen Dorpalen-Barry},
  journal = {arXiv 2104.02740},
  pages   = {1--16},
  title   = {The {V}archenko-{G}el'fand {R}ing of a {C}one},
  year    = {2021}
}

@article{DorpalenKimReiner,
  abstract      = {Hyperplane arrangements dissect {\$}{$\backslash$}mathbb {\{}R{\}}\^{}{\{}n{\}}{\$}into connected components called chambers, and a well-known theorem of Zaslavsky counts chambers as a sum of nonnegative integers called Whitney numbers of the first kind. His theorem generalizes to count chambers within any cone defined as the intersection of a collection of halfspaces from the arrangement, leading to a notion of Whitney numbers for each cone. This paper focuses on cones within the braid arrangement, consisting of the reflecting hyperplanes xi = xj inside {\$}{$\backslash$}mathbb {\{}R{\}}\^{}{\{}n{\}}{\$}for the symmetric group, thought of as the type An−1 reflection group. Here, cones correspond to posets,chambers within the cone correspond to linear extensions of the poset,the Whitney numbers of the cone interestingly refine the number of linear extensions of the poset.},
  author        = {Dorpalen-Barry, Galen and Kim, Jang Soo and Reiner, Victor},
  da            = {2021/01/25},
  date-added    = {2021-04-05 17:31:52 -0500},
  date-modified = {2021-04-05 17:32:10 -0500},
  doi           = {10.1007/s11083-020-09541-4},
  id            = {Dorpalen-Barry2021},
  isbn          = {1572-9273},
  journal       = {Order},
  title         = {Whitney {N}umbers for {P}oset {C}ones},
  ty            = {JOUR},
  url           = {https://doi.org/10.1007/s11083-020-09541-4},
  year          = {2021},
  bdsk-url-1    = {https://doi.org/10.1007/s11083-020-09541-4}
}

@article{duSautoy-Grunewald,
  author     = {du Sautoy, Marcus and Grunewald, Fritz J.},
  title      = {Analytic properties of zeta functions and subgroup growth},
  journal    = {Ann. of Math. (2)},
  fjournal   = {Annals of Mathematics. Second Series},
  volume     = {152},
  year       = {2000},
  number     = {3},
  pages      = {793--833},
  issn       = {0003-486X},
  mrclass    = {11M41 (20E07)},
  mrnumber   = {1815702},
  mrreviewer = {Alexander Lubotzky},
  doi        = {10.2307/2661355},
  url        = {https://doi.org/10.2307/2661355}
}

@book{ec1,
  address       = {New York, NY, USA},
  author        = {Stanley, Richard P.},
  date-added    = {2019-02-08 10:31:52 -0600},
  date-modified = {2019-02-08 10:31:52 -0600},
  edition       = {2},
  journal       = {Enumerative Combinatorics, Volume 1},
  publisher     = {Cambridge University Press},
  title         = {Enumerative {C}ombinatorics},
  year          = {2012}
}

@book{ec2,
  address       = {Cambridge, UK},
  author        = {Richard Stanley},
  date-added    = {2019-02-08 10:31:52 -0600},
  date-modified = {2019-02-08 10:31:52 -0600},
  publisher     = {Cambridge University Press},
  title         = {Enumerative {C}ombinatorics, Volume 2},
  year          = {1999}
}

@article{ehrenborg-poset-hopf,
  author     = {Ehrenborg, Richard},
  title      = {On posets and {H}opf algebras},
  journal    = {Adv. Math.},
  fjournal   = {Advances in Mathematics},
  volume     = {119},
  year       = {1996},
  number     = {1},
  pages      = {1--25},
  issn       = {0001-8708,1090-2082},
  mrclass    = {16W30 (06A07)},
  mrnumber   = {1383883},
  mrreviewer = {Volkmar\ Welker},
  doi        = {10.1006/aima.1996.0026},
  url        = {https://doi.org/10.1006/aima.1996.0026}
}

@article{ehrenborg-readdy,
  author     = {Ehrenborg, Richard and Readdy, Margaret},
  doi        = {10.1007/s11083-010-9182-0},
  fjournal   = {Order. A Journal on the Theory of Ordered Sets and its Applications},
  issn       = {0167-8094},
  journal    = {Order},
  mrclass    = {06A07 (05E45)},
  mrnumber   = {2851357},
  mrreviewer = {Du\v{s}ko Joji\'{c}},
  number     = {3},
  pages      = {437--442},
  title      = {On the non-existence of an {$R$}-labeling},
  url        = {https://doi.org/10.1007/s11083-010-9182-0},
  volume     = {28},
  year       = {2011},
  bdsk-url-1 = {https://doi.org/10.1007/s11083-010-9182-0}
}

@article{ehrenborg-readdy-coproducts,
  author     = {Ehrenborg, Richard and Readdy, Margaret},
  title      = {Coproducts and the {$cd$}-index},
  journal    = {J. Algebraic Combin.},
  fjournal   = {Journal of Algebraic Combinatorics. An International Journal},
  volume     = {8},
  year       = {1998},
  number     = {3},
  pages      = {273--299},
  issn       = {0925-9899,1572-9192},
  mrclass    = {52B05 (05A05 06A07 16W30 52B22)},
  mrnumber   = {1651249},
  mrreviewer = {G\'{a}bor\ Hetyei},
  doi        = {10.1023/A:1008614816374},
  url        = {https://doi.org/10.1023/A:1008614816374}
}

@article{Ehrenborg-Readdy-Slone,
  abstract      = {We extend the Billera--Ehrenborg--Readdy map between the intersection lattice and face lattice of a central hyperplane arrangement to affine and toric hyperplane arrangements. For arrangements on the torus, we also generalize Zaslavsky's fundamental results on the number of regions.},
  author        = {Ehrenborg, Richard and Readdy, Margaret and Slone, MLE},
  date          = {2009/06/01},
  date-added    = {2022-11-18 15:39:41 +0100},
  date-modified = {2022-11-18 15:39:41 +0100},
  doi           = {10.1007/s00454-009-9134-x},
  id            = {Ehrenborg2009},
  isbn          = {1432-0444},
  journal       = {Discrete \& Computational Geometry},
  number        = {4},
  pages         = {481--512},
  title         = {Affine and Toric Hyperplane Arrangements},
  url           = {https://doi.org/10.1007/s00454-009-9134-x},
  volume        = {41},
  year          = {2009},
  bdsk-url-1    = {https://doi.org/10.1007/s00454-009-9134-x}
}

@article{Ehrenborg-Readdy-transforms,
  author   = {Ehrenborg, Richard and Readdy, Margaret},
  title    = {The {T}chebyshev transforms of the first and second kind},
  journal  = {Ann. Comb.},
  fjournal = {Annals of Combinatorics},
  volume   = {14},
  year     = {2010},
  number   = {2},
  pages    = {211--244},
  issn     = {0218-0006,0219-3094},
  mrclass  = {05E15 (06A11 16T30)},
  mrnumber = {2653890},
  doi      = {10.1007/s00026-010-0057-2},
  url      = {https://doi.org/10.1007/s00026-010-0057-2}
}

@article{Ehrenborg-signed,
  author     = {Ehrenborg, Richard},
  title      = {The {$r$}-signed {B}irkhoff transform},
  journal    = {Discrete Math.},
  fjournal   = {Discrete Mathematics},
  volume     = {344},
  year       = {2021},
  number     = {2},
  issue      = {12},
  issn       = {0012-365X},
  mrclass    = {06D05 (06A07 06A11)},
  mrnumber   = {4176983},
  mrreviewer = {Hans Arwed Keller},
  doi        = {10.1016/j.disc.2020.112214},
  url        = {https://doi.org/10.1016/j.disc.2020.112214}
}

@book{eisenbud,
  author     = {Eisenbud, David},
  doi        = {10.1007/978-1-4612-5350-1},
  isbn       = {0-387-94268-8; 0-387-94269-6},
  mrclass    = {13-01 (14A05)},
  mrnumber   = {1322960},
  mrreviewer = {Matthew Miller},
  note       = {With a view toward algebraic geometry},
  pages      = {xvi+785},
  publisher  = {Springer-Verlag, New York},
  series     = {Graduate Texts in Mathematics},
  title      = {Commutative {A}lgebra},
  url        = {https://doi.org/10.1007/978-1-4612-5350-1},
  volume     = {150},
  year       = {1995},
  bdsk-url-1 = {https://doi.org/10.1007/978-1-4612-5350-1}
}

@article{fishel,
  author     = {Fishel, Susanna},
  booktitle  = {Recent {T}rends in {A}lgebraic {C}ombinatorics},
  doi        = {10.1007/978-3-030-05141-9\_3},
  mrclass    = {05E15 (05A17 52C35)},
  mrnumber   = {3969572},
  mrreviewer = {Ricardo Mamede},
  pages      = {75--113},
  publisher  = {Springer, Cham},
  series     = {Assoc. Women Math. Ser.},
  title      = {A {S}urvey of the {S}hi {A}rrangement},
  url        = {https://doi-org.ezp3.lib.umn.edu/10.1007/978-3-030-05141-9_3},
  volume     = {16},
  year       = {2019},
  bdsk-url-1 = {https://doi-org.ezp3.lib.umn.edu/10.1007/978-3-030-05141-9_3}
}

@book{foata,
  address       = {Lecture Notes in Mathematics},
  author        = {Dominique Foata and Pierre Cartier},
  date-added    = {2019-02-08 10:31:52 -0600},
  date-modified = {2019-02-08 10:31:52 -0600},
  publisher     = {Springer Verlag},
  title         = {Probl{\`e}mes {C}ombinatoires de {C}ommutation et {R}{\'e}arrangements},
  year          = {1969}
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@article{foata-zeilberger,
  author     = {Foata, Dominique and Zeilberger, Doron},
  doi        = {10.1137/0401043},
  fjournal   = {SIAM Journal on Discrete Mathematics},
  issn       = {0895-4801},
  journal    = {SIAM J. Discrete Math.},
  mrclass    = {05A15 (33A65)},
  mrnumber   = {968850},
  mrreviewer = {R. A. Askey},
  number     = {4},
  pages      = {425--433},
  title      = {Laguerre {P}olynomials, weighted {D}erangements, and {P}ositivity},
  url        = {https://doi.org/10.1137/0401043},
  volume     = {1},
  year       = {1988},
  bdsk-url-1 = {https://doi.org/10.1137/0401043}
}

@phdthesis{foatathesis,
  author        = {Dominique Foata},
  date-added    = {2019-02-08 10:31:52 -0600},
  date-modified = {2019-02-08 10:31:52 -0600},
  school        = {Publ. Inst. Statist. Univ. Paris},
  title         = {Etude {A}lg{\'e}brique de {C}ertains {P}robl{\`e}mes d'analyse {C}ombinatoire et du {C}alcul des {P}robabilit{\'e}s},
  year          = {1965}
}

@article{froberg75,
  author     = {Fr\"{o}berg, Ralph},
  doi        = {10.7146/math.scand.a-11585},
  fjournal   = {Mathematica Scandinavica},
  issn       = {0025-5521},
  journal    = {Math. Scand.},
  mrclass    = {13H99},
  mrnumber   = {404254},
  mrreviewer = {M. Nagata},
  number     = {1},
  pages      = {29--39},
  title      = {Determination of a {C}lass of {P}oincar\'{e} {S}eries},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.7146/math.scand.a-11585},
  volume     = {37},
  year       = {1975},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.7146/math.scand.a-11585},
  bdsk-url-2 = {https://doi.org/10.7146/math.scand.a-11585}
}

@book{froberg97,
  author     = {Fr\"{o}berg, R.},
  booktitle  = {Advances in {C}ommutative {R}ing {T}heory ({F}ez, 1997)},
  mrclass    = {16S37 (13D02)},
  mrnumber   = {1767430},
  mrreviewer = {Lidia Angeleri H\"{u}gel},
  pages      = {337--350},
  publisher  = {Dekker, New York},
  series     = {Lecture Notes in Pure and Appl. Math.},
  title      = {Koszul {A}lgebras},
  volume     = {205},
  year       = {1999}
}

@article{garoufalidis,
  author        = {Stavros Garoufalidis and Thang T.Q. L{\^e} and Doron Zeilberger},
  date-added    = {2019-02-08 10:31:52 -0600},
  date-modified = {2019-02-08 10:31:52 -0600},
  journal       = {J. Algebra},
  month         = {March},
  title         = {The {Q}uantum {M}ac{M}ahon {M}aster {T}heorem},
  year          = {2003}
}

@article{gelfand,
  author        = {A. N. Varchenko and I. M. Gel'fand},
  date-added    = {2019-02-08 10:31:52 -0600},
  date-modified = {2019-02-08 10:31:52 -0600},
  journal       = {Functional Analysis and Its Applications},
  number        = {4},
  pages         = {255-270},
  title         = {Heaviside {F}unctions of a {C}onfiguration of {H}yperplanes},
  volume        = {21},
  year          = {1988}
}

@article{gelfand-et-al-noncommutative,
  title   = {Noncommutative Symmetrical Functions},
  journal = {Advances in Mathematics},
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  number  = {2},
  pages   = {218-348},
  year    = {1995},
  issn    = {0001-8708},
  doi     = {https://doi.org/10.1006/aima.1995.1032},
  url     = {https://www.sciencedirect.com/science/article/pii/S0001870885710328},
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@article{GelfandRybnikov,
  author     = {Gel'fand, I. M. and Rybnikov, G. L.},
  fjournal   = {Doklady Akademii Nauk SSSR},
  issn       = {0002-3264},
  journal    = {Dokl. Akad. Nauk SSSR},
  mrclass    = {32C40 (05B35)},
  mrnumber   = {1020668},
  mrreviewer = {Gerhard Pfister},
  number     = {4},
  pages      = {791--795},
  title      = {Algebraic and {T}opological {I}nvariants of {O}riented {M}atroids},
  volume     = {307},
  year       = {1989}
}

@phdthesis{gente,
  author        = {Regina Gente},
  date-added    = {2019-02-08 10:31:52 -0600},
  date-modified = {2019-02-08 10:31:52 -0600},
  school        = {Universit\"{a}t Marburg},
  title         = {The {V}archenko {M}atrix for {C}ones},
  year          = {2013}
}

@article{gessel,
  author     = {Gessel, Ira M.},
  booktitle  = {Combinatorics and {A}lgebra ({B}oulder, {C}olo., 1983)},
  doi        = {10.1090/conm/034/777705},
  mrclass    = {05A17 (20C30)},
  mrnumber   = {777705},
  mrreviewer = {J. D\'{e}sarm\'{e}nien},
  pages      = {289--317},
  publisher  = {Amer. Math. Soc., Providence, RI},
  series     = {Contemp. Math.},
  title      = {Multipartite {$P$}-partitions and {I}nner {P}roducts of {S}kew {S}chur functions},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.1090/conm/034/777705},
  volume     = {34},
  year       = {1984},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.1090/conm/034/777705},
  bdsk-url-2 = {https://doi.org/10.1090/conm/034/777705}
}

@article{gordan,
  author     = {Gordan, P.},
  doi        = {10.1007/BF01442864},
  fjournal   = {Mathematische Annalen},
  issn       = {0025-5831},
  journal    = {Math. Ann.},
  mrclass    = {DML},
  mrnumber   = {1509805},
  number     = {1},
  pages      = {23--28},
  title      = {Ueber die {A}ufl\"{o}sung {L}inearer {G}leichungen mit reellen {C}oefficienten},
  url        = {https://doi.org/10.1007/BF01442864},
  volume     = {6},
  year       = {1873},
  bdsk-url-1 = {https://doi.org/10.1007/BF01442864}
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@article{Grunewald-Segal-Smith,
  author     = {Grunewald, Fritz J. and Segal, Daniel M. and Smith, Geoff C.},
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  volume     = {93},
  year       = {1988},
  number     = {1},
  pages      = {185--223},
  issn       = {0020-9910},
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  mrnumber   = {943928},
  mrreviewer = {Daniel Barsky},
  doi        = {10.1007/BF01393692},
  url        = {https://doi.org/10.1007/BF01393692}
}

@article{haiman,
  author     = {Haiman, Mark},
  doi        = {10.1007/s002220200219},
  fjournal   = {Inventiones Mathematicae},
  issn       = {0020-9910},
  journal    = {Invent. Math.},
  mrclass    = {14C05 (05E05 14F17 14R20)},
  mrnumber   = {1918676},
  mrreviewer = {Claudio Procesi},
  number     = {2},
  pages      = {371--407},
  title      = {Vanishing theorems and character formulas for the {H}ilbert scheme of points in the plane},
  url        = {https://doi.org/10.1007/s002220200219},
  volume     = {149},
  year       = {2002},
  bdsk-url-1 = {https://doi.org/10.1007/s002220200219}
}

@article{Hsiao,
  author     = {Hsiao, Samuel K.},
  title      = {A signed analog of the {B}irkhoff transform},
  journal    = {J. Combin. Theory Ser. A},
  fjournal   = {Journal of Combinatorial Theory. Series A},
  volume     = {113},
  year       = {2006},
  number     = {2},
  pages      = {251--272},
  issn       = {0097-3165},
  mrclass    = {05B35 (06A07)},
  mrnumber   = {2199274},
  mrreviewer = {G\'{a}bor Hetyei},
  doi        = {10.1016/j.jcta.2005.03.003},
  url        = {https://doi.org/10.1016/j.jcta.2005.03.003}
}

@book{humphreys,
  author     = {Humphreys, James E.},
  doi        = {10.1017/CBO9780511623646},
  isbn       = {0-521-37510-X},
  mrclass    = {20-02 (20F32 20F55 20G15 20H15)},
  mrnumber   = {1066460},
  mrreviewer = {Louis Solomon},
  pages      = {xii+204},
  publisher  = {Cambridge University Press, Cambridge},
  series     = {Cambridge Studies in Advanced Mathematics},
  title      = {Reflection {G}roups and {C}oxeter {G}roups},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.1017/CBO9780511623646},
  volume     = {29},
  year       = {1990},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.1017/CBO9780511623646},
  bdsk-url-2 = {https://doi.org/10.1017/CBO9780511623646}
}

@article{Jensen-Kutler-Usatine,
  author     = {Jensen, David and Kutler, Max and Usatine, Jeremy},
  title      = {The motivic zeta functions of a matroid},
  journal    = {J. Lond. Math. Soc. (2)},
  fjournal   = {Journal of the London Mathematical Society. Second Series},
  volume     = {103},
  year       = {2021},
  number     = {2},
  pages      = {604--632},
  issn       = {0024-6107,1469-7750},
  mrclass    = {05B35 (14E18 14T15)},
  mrnumber   = {4230913},
  mrreviewer = {Laura\ Bertani},
  doi        = {10.1112/jlms.12386},
  url        = {https://doi.org/10.1112/jlms.12386}
}

@incollection{joni-rota,
  author    = {Joni, S. A. and Rota, G.-C.},
  title     = {Coalgebras and bialgebras in combinatorics},
  booktitle = {Umbral calculus and {H}opf algebras ({N}orman, {O}kla., 1978)},
  series    = {Contemp. Math.},
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  publisher = {Amer. Math. Soc., Providence, RI},
  year      = {1982},
  isbn      = {0-8218-5003-2},
  mrclass   = {05A10 (16A24)},
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@article{karu,
  author     = {Karu, Kalle},
  doi        = {10.1112/S0010437X06001928},
  journal    = {Compositio Mathematica},
  number     = {3},
  pages      = {701--718},
  publisher  = {London Mathematical Society},
  title      = {The cd-index of fans and posets},
  volume     = {142},
  year       = {2006},
  bdsk-url-1 = {https://doi.org/10.1112/S0010437X06001928}
}

@book{knuth,
  author        = {Donald Ervin Knuth},
  date-added    = {2019-02-08 10:31:52 -0600},
  date-modified = {2019-02-08 10:31:52 -0600},
  publisher     = {Addison-Wesley},
  title         = {The {A}rt of {C}omputer {P}rogramming},
  year          = {2015}
}


@article{Konvalinka,
  author        = {Matjaz Konvalinka and Igor Pak},
  date-added    = {2019-02-08 10:31:52 -0600},
  date-modified = {2019-02-08 10:31:52 -0600},
  journal       = {Advances in Mathematics},
  title         = {Non-Commutative {E}xtensions of {M}ac{M}ahon's {M}aster {T}heorem},
  year          = {2007}
}


@article{Kuhne-Maglione,
  author    = {K\"uhne, Lukas and Maglione, Joshua},
  title     = {On the geometry of flag {Hilbert{\textendash}Poincar\'e} series for matroids},
  journal   = {Algebraic Combinatorics},
  pages     = {623--638},
  publisher = {The Combinatorics Consortium},
  volume    = {6},
  number    = {3},
  year      = {2023},
  doi       = {10.5802/alco.276},
  language  = {en},
  url       = {https://alco.centre-mersenne.org/articles/10.5802/alco.276/}
}

@article{lam-postnikov,
  author     = {Lam, Thomas and Postnikov, Alexander},
  doi        = {10.1007/s00454-006-1294-3},
  fjournal   = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science},
  issn       = {0179-5376},
  journal    = {Discrete Comput. Geom.},
  mrclass    = {52B12 (52B40)},
  mrnumber   = {2352704},
  mrreviewer = {Jes\'{u}s A. De Loera},
  number     = {3},
  pages      = {453--478},
  title      = {Alcoved polytopes. {I}},
  url        = {https://doi.org/10.1007/s00454-006-1294-3},
  volume     = {38},
  year       = {2007},
  bdsk-url-1 = {https://doi.org/10.1007/s00454-006-1294-3}
}

@incollection{lam-postnikov2,
  author     = {Lam, Thomas and Postnikov, Alexander},
  booktitle  = {Lie groups, geometry, and representation theory},
  mrclass    = {52B12 (05E10 20F55)},
  mrnumber   = {3890212},
  mrreviewer = {Gabriel K. Cunningham},
  pages      = {253--272},
  publisher  = {Birkh\"{a}user/Springer, Cham},
  series     = {Progr. Math.},
  title      = {Alcoved polytopes {II}},
  volume     = {326},
  year       = {2018}
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@article{lehrer-solomon,
  author     = {Lehrer, G. I. and Solomon, Louis},
  doi        = {10.1016/0021-8693(86)90225-5},
  fjournal   = {Journal of Algebra},
  issn       = {0021-8693},
  journal    = {J. Algebra},
  mrclass    = {32C40 (20C30 32B30)},
  mrnumber   = {866785},
  mrreviewer = {Hiroaki Terao},
  number     = {2},
  pages      = {410--424},
  title      = {On the {A}ction of the {S}ymmetric {G}roup on the {C}ohomology of the {C}omplement of its {R}eflecting {H}yperplanes},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.1016/0021-8693(86)90225-5},
  volume     = {104},
  year       = {1986},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.1016/0021-8693(86)90225-5},
  bdsk-url-2 = {https://doi.org/10.1016/0021-8693(86)90225-5}
}

@article{lofwall,
  author     = {L\"{o}fwall, Clas},
  booktitle  = {Algebra, {A}lgebraic {T}opology and their {I}nteractions},
  doi        = {10.1007/BFb0075468},
  mrclass    = {16A61 (13D99 18G15)},
  mrnumber   = {846457},
  mrreviewer = {Kenneth A. Brown},
  pages      = {291--338},
  publisher  = {Springer, Berlin},
  series     = {Lecture Notes in Math.},
  title      = {On the {S}ubalgebra {G}enerated by the {O}ne-{D}imensional {E}lements in the {Y}oneda {E}xt-algebra},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.1007/BFb0075468},
  volume     = {1183},
  year       = {1986},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.1007/BFb0075468},
  bdsk-url-2 = {https://doi.org/10.1007/BFb0075468}
}

@incollection{lubotzky-survey,
  author     = {Lubotzky, Alexander},
  title      = {Counting finite index subgroups},
  booktitle  = {Groups '93 {G}alway/{S}t. {A}ndrews, {V}ol. 2},
  series     = {London Math. Soc. Lecture Note Ser.},
  volume     = {212},
  pages      = {368--404},
  publisher  = {Cambridge Univ. Press, Cambridge},
  year       = {1995},
  mrclass    = {20F99 (11M41 20H05)},
  mrnumber   = {1337284},
  mrreviewer = {Marcus du Sautoy},
  doi        = {10.1017/CBO9780511629297.008},
  url        = {https://doi.org/10.1017/CBO9780511629297.008}
}

@article{macauley,
  author        = {Matthew Macauley},
  date-added    = {2019-02-09 11:41:58 -0600},
  date-modified = {2019-02-09 11:43:41 -0600},
  month         = {June},
  number        = {39},
  title         = {Morphisms and {O}rder {I}deals of {T}oric {P}osets},
  volume        = {4},
  year          = {2016}
}

@article{Maglione-Voll,
  author        = {Maglione, Joshua and Voll, Christopher},
  date-added    = {2023-01-10 18:59:18 +0100},
  date-modified = {2023-01-10 19:00:45 +0100},
  journal       = {Israel Journal of Mathematics (to appear)},
  title         = {Flag {H}ilbert--{P}oincar{\'e} series of hyperplane arrangements and {I}gusa zeta functions},
  year          = {2023}
}

@book{mandel,
  author     = {Mandel, Arnaldo},
  isbn       = {978-0315-11027-4},
  mrclass    = {Thesis},
  mrnumber   = {2632449},
  note       = {Thesis (Ph.D.)--University of Waterloo (Canada)},
  pages      = {(no paging)},
  publisher  = {ProQuest LLC, Ann Arbor, MI},
  title      = {Topology of {O}riented {M}atroids},
  url        = {http://gateway.proquest.com.ezp2.lib.umn.edu/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:NK58940},
  year       = {1982},
  bdsk-url-1 = {http://gateway.proquest.com.ezp2.lib.umn.edu/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:NK58940}
}

@article {McMullen,
    AUTHOR = {McMullen, P.},
     TITLE = {The maximum numbers of faces of a convex polytope},
   JOURNAL = {Mathematika},
  FJOURNAL = {Mathematika. A Journal of Pure and Applied Mathematics},
    VOLUME = {17},
      YEAR = {1970},
     PAGES = {179--184},
      ISSN = {0025-5793},
   MRCLASS = {52.10},
  MRNUMBER = {283691},
MRREVIEWER = {G.\ T.\ Sallee},
       DOI = {10.1112/S0025579300002850},
       URL = {https://doi.org/10.1112/S0025579300002850},
}

@article{McNamara,
  abstract   = {It is well known that if a finite graded lattice of rank n is supersolvable, then it has an EL-labeling where the labels along any maximal chain form a permutation. We call such a labeling an Sn EL-labeling and we show that a finite graded lattice of rank n is supersolvable if and only if it has such a labeling. We next consider finite graded posets of rank n with 0̂ and 1̂ that have an Sn EL-labeling. We describe a type A 0-Hecke algebra action on the maximal chains of such posets. This action is local and gives a representation of these Hecke algebras whose character has characteristic that is closely related to Ehrenborg's flag quasisymmetric function. We ask what other classes of posets have such an action and in particular we show that finite graded lattices of rank n have such an action if and only if they have an Sn EL-labeling.},
  author     = {Peter McNamara},
  doi        = {https://doi.org/10.1016/S0097-3165(02)00019-5},
  issn       = {0097-3165},
  journal    = {Journal of Combinatorial Theory, Series A},
  keywords   = {Poset, Lattice, EL-labeling, Supersolvable lattice, Hecke algebra action, Quasisymmetric function},
  number     = {1},
  pages      = {69-89},
  title      = {EL-labelings, supersolvability and 0-Hecke algebra actions on posets},
  url        = {https://www.sciencedirect.com/science/article/pii/S0097316502000195},
  volume     = {101},
  year       = {2003},
  bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0097316502000195},
  bdsk-url-2 = {https://doi.org/10.1016/S0097-3165(02)00019-5}
}



@phdthesis{Meisinger,
  author    = {G{\"{u}}nter Meisinger},
  title     = {Flag numbers and quotients of convex polytopes},
  school    = {University of Passau, Germany},
  year      = {1994},
  url       = {https://d-nb.info/940956500},
  isbn      = {978-3-926931-19-1},
  timestamp = {Sat, 17 Jul 2021 09:03:05 +0200},
  biburl    = {https://dblp.org/rec/phd/dnb/Meisinger94.bib},
  bibsource = {dblp computer science bibliography, https://dblp.org}
}

@article{moseley,
  author     = {Moseley, Daniel},
  doi        = {10.1016/j.jalgebra.2016.10.010},
  fjournal   = {Journal of Algebra},
  issn       = {0021-8693},
  journal    = {J. Algebra},
  mrclass    = {52C35 (55R80)},
  mrnumber   = {3584871},
  mrreviewer = {Sadok Kallel},
  pages      = {95--114},
  title      = {Equivariant {C}ohomology and the {V}archenko-{G}elfand {F}iltration},
  url        = {https://doi.org/10.1016/j.jalgebra.2016.10.010},
  volume     = {472},
  year       = {2017},
  bdsk-url-1 = {https://doi.org/10.1016/j.jalgebra.2016.10.010}
}

@article{narayana,
  author     = {Venkata Narayana, Tadepalli},
  journal    = {C. R. Acad. Sci. Paris},
  mrclass    = {10.0X},
  mrnumber   = {0070648},
  mrreviewer = {H. Bergstr\"{o}m},
  pages      = {1188--1189},
  title      = {Sur les treillis form\'{e}s par les partitions d'un entier et leurs applications \`a la th\'{e}orie des probabilit\'{e}s},
  volume     = {240},
  year       = {1955}
}

@article{orlik-solomon,
  author     = {Orlik, Peter and Solomon, Louis},
  doi        = {10.1007/BF01390316},
  fjournal   = {Inventiones Mathematicae},
  issn       = {0020-9910},
  journal    = {Invent. Math.},
  mrclass    = {32C40 (57S17)},
  mrnumber   = {575083},
  mrreviewer = {Peter Giblin},
  number     = {1},
  pages      = {77--94},
  title      = {Unitary {R}eflection {G}roups and {C}ohomology},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.1007/BF01390316},
  volume     = {59},
  year       = {1980},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.1007/BF01390316},
  bdsk-url-2 = {https://doi.org/10.1007/BF01390316}
}

@book{OrlikTerao,
  author     = {Orlik, Peter and Terao, Hiroaki},
  doi        = {10.1007/978-3-662-02772-1},
  isbn       = {3-540-55259-6},
  mrclass    = {52B30 (14F35 20F36 20F55 32S25 57N65)},
  mrnumber   = {1217488},
  mrreviewer = {Michel Yves Jambu},
  pages      = {xviii+325},
  publisher  = {Springer-Verlag, Berlin},
  series     = {Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]},
  title      = {Arrangements of {H}yperplanes},
  url        = {https://doi.org/10.1007/978-3-662-02772-1},
  volume     = {300},
  year       = {1992},
  bdsk-url-1 = {https://doi.org/10.1007/978-3-662-02772-1}
}

@article{peeva,
  author     = {Peeva, Irena},
  doi        = {10.1090/S0002-9947-02-03128-8},
  fjournal   = {Transactions of the American Mathematical Society},
  issn       = {0002-9947},
  journal    = {Trans. Amer. Math. Soc.},
  mrclass    = {13D02 (52C35)},
  mrnumber   = {1932716},
  mrreviewer = {Daniel C. Cohen},
  number     = {2},
  pages      = {609--618},
  title      = {Hyperplane {A}rrangements and {L}inear {S}trands in {R}esolutions},
  url        = {https://doi.org/10.1090/S0002-9947-02-03128-8},
  volume     = {355},
  year       = {2003},
  bdsk-url-1 = {https://doi.org/10.1090/S0002-9947-02-03128-8}
}

@book{petersen,
  author     = {Petersen, T. Kyle},
  doi        = {10.1007/978-1-4939-3091-3},
  isbn       = {978-1-4939-3090-6; 978-1-4939-3091-3},
  mrclass    = {05-02 (05A15 05Exx 06A07 11B65 11B75 20F55)},
  mrnumber   = {3408615},
  mrreviewer = {Damir Yeliussizov},
  note       = {With a foreword by Richard Stanley},
  pages      = {xviii+456},
  publisher  = {Birkh\"{a}user/Springer, New York},
  series     = {Birkh\"{a}user Advanced Texts: Basler Lehrb\"{u}cher. [Birkh\"{a}user Advanced Texts: Basel Textbooks]},
  title      = {Eulerian numbers},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.1007/978-1-4939-3091-3},
  year       = {2015},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.1007/978-1-4939-3091-3},
  bdsk-url-2 = {https://doi.org/10.1007/978-1-4939-3091-3}
}

@article{postnikovreinerwilliams,
  author        = {Alexander Postnikov and Victor Reiner and Lauren Williams},
  date-added    = {2019-02-08 10:31:52 -0600},
  date-modified = {2019-02-08 10:31:52 -0600},
  journal       = {Documenta Mathematica},
  pages         = {207-273},
  title         = {Faces of {G}eneralized {P}ermutohedra},
  volume        = {13},
  year          = {2008}
}

@article{proudfoot,
  author     = {Proudfoot, Nicholas},
  doi        = {10.1016/j.jalgebra.2006.08.013},
  fjournal   = {Journal of Algebra},
  issn       = {0021-8693},
  journal    = {J. Algebra},
  mrclass    = {05B35 (32S22)},
  mrnumber   = {2266876},
  mrreviewer = {Michael J. Falk},
  number     = {2},
  pages      = {1186--1196},
  title      = {The {E}quivariant {O}rlik-{S}olomon {A}lgebra},
  url        = {https://doi.org/10.1016/j.jalgebra.2006.08.013},
  volume     = {305},
  year       = {2006},
  bdsk-url-1 = {https://doi.org/10.1016/j.jalgebra.2006.08.013}
}

@article{Purtill,
  author     = {Purtill, Mark},
  doi        = {10.2307/2154445},
  fjournal   = {Transactions of the American Mathematical Society},
  issn       = {0002-9947},
  journal    = {Trans. Amer. Math. Soc.},
  mrclass    = {52B05 (05E15 06A08)},
  mrnumber   = {1094560},
  mrreviewer = {Margaret M. Bayer},
  number     = {1},
  pages      = {77--104},
  title      = {Andr\'{e} permutations, lexicographic shellability and the {$cd$}-index of a convex polytope},
  url        = {https://doi.org/10.2307/2154445},
  volume     = {338},
  year       = {1993},
  bdsk-url-1 = {https://doi.org/10.2307/2154445}
}

@article{reiner,
  author     = {Reiner, Victor},
  doi        = {10.1090/memo/0460},
  fjournal   = {Memoirs of the American Mathematical Society},
  issn       = {0065-9266},
  journal    = {Mem. Amer. Math. Soc.},
  mrclass    = {05E10 (13A50 20F55 52B20)},
  mrnumber   = {1101971},
  mrreviewer = {Ira Gessel},
  number     = {460},
  pages      = {vi+134},
  title      = {Quotients of {C}oxeter {C}omplexes and {$P$}-partitions},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.1090/memo/0460},
  volume     = {95},
  year       = {1992},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.1090/memo/0460},
  bdsk-url-2 = {https://doi.org/10.1090/memo/0460}
}

@article{reiner-welker,
  author        = {Victor Reiner and Volkmar Welker},
  date-added    = {2019-02-08 10:31:52 -0600},
  date-modified = {2019-02-08 10:31:52 -0600},
  journal       = {Journal of Combinatorial Theory, Series A},
  month         = {February},
  number        = {2},
  pages         = {247-280},
  title         = {On the {C}harney-{D}avis and {N}eggers-{S}tanley Conjectures},
  volume        = {109},
  year          = {2005}
}

@article{reiner93,
  author     = {Reiner, Victor},
  doi        = {10.1016/0097-3165(93)90052-A},
  fjournal   = {Journal of Combinatorial Theory. Series A},
  issn       = {0097-3165},
  journal    = {J. Combin. Theory Ser. A},
  mrclass    = {06A07 (05E99)},
  mrnumber   = {1207741},
  mrreviewer = {Sergey V. Fomin},
  number     = {2},
  pages      = {324--360},
  title      = {Signed {P}osets},
  url        = {https://doi-org.ezp1.lib.umn.edu/10.1016/0097-3165(93)90052-A},
  volume     = {62},
  year       = {1993},
  bdsk-url-1 = {https://doi-org.ezp1.lib.umn.edu/10.1016/0097-3165(93)90052-A},
  bdsk-url-2 = {https://doi.org/10.1016/0097-3165(93)90052-A}
}

@article{reiner93a,
  author     = {Reiner, Victor},
  title      = {Signed permutation statistics},
  journal    = {European J. Combin.},
  fjournal   = {European Journal of Combinatorics},
  volume     = {14},
  year       = {1993},
  number     = {6},
  pages      = {553--567},
  issn       = {0195-6698},
  mrclass    = {05A15 (05E05)},
  mrnumber   = {1248063},
  mrreviewer = {Edward E. Allen},
  doi        = {10.1006/eujc.1993.1058},
  url        = {https://doi.org/10.1006/eujc.1993.1058}
}

@article{reiner97,
  author     = {Reiner, Victor},
  doi        = {10.1016/S0012-365X(96)00365-2},
  fjournal   = {Discrete Mathematics},
  issn       = {0012-365X},
  journal    = {Discrete Math.},
  mrclass    = {06A07 (05A18 05E15)},
  mrnumber   = {1483446},
  mrreviewer = {Darla Kremer},
  number     = {1-3},
  pages      = {195--222},
  title      = {Non-crossing partitions for classical reflection groups},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.1016/S0012-365X(96)00365-2},
  volume     = {177},
  year       = {1997},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.1016/S0012-365X(96)00365-2},
  bdsk-url-2 = {https://doi.org/10.1016/S0012-365X(96)00365-2}
}

@article{Renyi,
  author     = {R\'{e}nyi, Alfr\'{e}d},
  fjournal   = {Annales de la Facult\'{e} des Sciences de l'Universit\'{e} de Clermont-Ferrand},
  issn       = {0069-472X},
  journal    = {Ann. Fac. Sci. Univ. Clermont-Ferrand},
  mrclass    = {60.30},
  mrnumber   = {286162},
  mrreviewer = {R. Fischler},
  pages      = {7--13},
  title      = {Th\'{e}orie des \'{e}l\'{e}ments saillants d'une suite d'observations},
  volume     = {8},
  year       = {1962}
}

@book{richter-gebert-ziegler,
  editor     = {Goodman, Jacob E. and O'Rourke, Joseph and T\'{o}th, Csaba D.},
  isbn       = {978-1-4987-1139-5},
  mrclass    = {52-00 (00A20 05B25 65D18 68-06)},
  mrnumber   = {3793131},
  mrreviewer = {Egon Schulte},
  pages      = {xxi+1927},
  publisher  = {CRC Press, Boca Raton, FL},
  series     = {Discrete Mathematics and its Applications (Boca Raton)},
  title      = {Handbook of {D}iscrete and {C}omputational {G}eometry},
  year       = {2018}
}

@article{Rossmann,
  author     = {Rossmann, Tobias},
  title      = {Computing topological zeta functions of groups, algebras, and
                modules, {I}},
  journal    = {Proc. Lond. Math. Soc. (3)},
  fjournal   = {Proceedings of the London Mathematical Society. Third Series},
  volume     = {110},
  year       = {2015},
  number     = {5},
  pages      = {1099--1134},
  issn       = {0024-6115,1460-244X},
  mrclass    = {11M41 (14E18 14G10 17A01 20F69 52B20)},
  mrnumber   = {3349788},
  mrreviewer = {Michael\ M.\ Schein},
  doi        = {10.1112/plms/pdv012},
  url        = {https://doi.org/10.1112/plms/pdv012}
}

@misc{Rossmann-Voll,
  author     = {Rossmann, Tobias and Voll, Christopher},
  copyright  = {arXiv.org perpetual, non-exclusive license},
  doi        = {10.48550/arXiv.1908.09589},
  keywords   = {Group Theory (math.GR), FOS: Mathematics, FOS: Mathematics, 11M41, 20D15, 20E45, 15B33, 05A15, 05C50, 14M25, 11S80},
  publisher  = {arXiv},
  title      = {Groups, graphs, and hypergraphs: average sizes of kernels of generic matrices with support constraints},
  url        = {https://arxiv.org/abs/1908.09589},
  year       = {2019},
  note       = {to appear in Mem. Amer. Math. Soc.},
  bdsk-url-1 = { https://arxiv.org/abs/1908.09589  },
  bdsk-url-2 = {https://doi.org/ 10.48550/arXiv.1908.09589  }
}

@article{rota,
  author     = {Rota, Gian-Carlo},
  doi        = {10.1007/BF00531932},
  fjournal   = {Zeitschrift f\"{u}r Wahrscheinlichkeitstheorie und Verwandte Gebiete},
  journal    = {Z. Wahrscheinlichkeitstheorie und Verw. Gebiete},
  mrclass    = {05.05},
  mrnumber   = {174487},
  mrreviewer = {M. A. Harrison},
  pages      = {340--368 (1964)},
  title      = {On the {F}oundations of {C}ombinatorial {T}heory. {I}. {T}heory of {M}\"{o}bius functions},
  url        = {https://doi.org/10.1007/BF00531932},
  volume     = {2},
  year       = {1964},
  bdsk-url-1 = {https://doi.org/10.1007/BF00531932}
}

@article{RSW,
  author   = {Reiner, Victor and Saliola, Franco and Welker, Volkmar},
  fjournal = {Memoirs of the American Mathematical Society},
  isbn     = {978-0-8218-9095-0},
  issn     = {0065-9266},
  journal  = {Mem. Amer. Math. Soc.},
  mrclass  = {05E15 (20F55 62Qxx)},
  mrnumber = {3184410},
  number   = {1072},
  pages    = {vi+109},
  title    = {Spectra of {S}ymmetrized {S}huffling {O}perators},
  volume   = {228},
  year     = {2014}
}

@article{sagan,
  author     = {Sagan, Bruce E.},
  doi        = {10.1006/aima.1995.1021},
  fjournal   = {Advances in Mathematics},
  issn       = {0001-8708},
  journal    = {Adv. Math.},
  mrclass    = {05B35 (05A15 05E15 06A07 06C10)},
  mrnumber   = {1318527},
  mrreviewer = {Joseph Kung},
  number     = {2},
  pages      = {195--207},
  title      = {A {G}eneralization of {R}ota's {NBC} theorem},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.1006/aima.1995.1021},
  volume     = {111},
  year       = {1995},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.1006/aima.1995.1021},
  bdsk-url-2 = {https://doi.org/10.1006/aima.1995.1021}
}

@manual{sagemath,
  author = {{The Sage Developers}},
  key    = {SageMath},
  note   = {{\tt https://www.sagemath.org}},
  title  = {{S}ageMath, the {S}age {M}athematics {S}oftware {S}ystem ({V}ersion 9.2)},
  year   = {2021}
}

@article{saito,
  author     = {Saito, Kyoji},
  doi        = {10.1016/j.aim.2006.11.002},
  fjournal   = {Advances in Mathematics},
  issn       = {0001-8708},
  journal    = {Adv. Math.},
  mrclass    = {52B05 (05C05 20F36)},
  mrnumber   = {2329315},
  number     = {2},
  pages      = {645--668},
  title      = {Principal {$\Gamma$}-cone for a {T}ree},
  url        = {https://doi.org/10.1016/j.aim.2006.11.002},
  volume     = {212},
  year       = {2007},
  bdsk-url-1 = {https://doi.org/10.1016/j.aim.2006.11.002}
}

@article{saliola-thomas,
  abstract      = {We propose a definition of an oriented interval greedoid that simultaneously generalizes the notion of an oriented matroid and the construction on antimatroids introduced by L.J. Billera, S.K. Hsiao, and J.S. Provan in Enumeration in convex geometries and associated polytopal subdivisions of spheres (Discrete Comput. Geom. 39(1--3):123--137, 2008). As for oriented matroids, associated to each oriented interval greedoid is a spherical simplicial complex whose face enumeration depends only on the underlying interval greedoid.},
  author        = {Saliola, Franco and Thomas, Hugh},
  date          = {2012/01/01},
  date-added    = {2022-11-18 15:48:21 +0100},
  date-modified = {2022-11-18 15:48:21 +0100},
  doi           = {10.1007/s00454-011-9383-3},
  id            = {Saliola2012},
  isbn          = {1432-0444},
  journal       = {Discrete \& Computational Geometry},
  number        = {1},
  pages         = {64--105},
  title         = {Oriented Interval Greedoids},
  url           = {https://doi.org/10.1007/s00454-011-9383-3},
  volume        = {47},
  year          = {2012},
  bdsk-url-1    = {https://doi.org/10.1007/s00454-011-9383-3}
}


@article{shi,
  author     = {Shi, Jian Yi},
  doi        = {10.1112/jlms/s2-35.1.42},
  fjournal   = {Journal of the London Mathematical Society. Second Series},
  issn       = {0024-6107},
  journal    = {J. London Math. Soc. (2)},
  mrclass    = {20H15 (17B10 20G05)},
  mrnumber   = {871764},
  mrreviewer = {D.-N. Verma},
  number     = {1},
  pages      = {42--55},
  title      = {Alcoves corresponding to an affine {W}eyl group},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.1112/jlms/s2-35.1.42},
  volume     = {35},
  year       = {1987},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.1112/jlms/s2-35.1.42},
  bdsk-url-2 = {https://doi.org/10.1112/jlms/s2-35.1.42}
}

@article{stanley-cmcxs,
  author  = {Stanley, Richard P.},
  journal = {Trans. Amer. Math. Soc.},
  pages   = {139--157},
  title   = {{B}alanced {C}ohen-Macaulay complexes},
  volume  = {249(1)},
  year    = {1979}
}

@article{stanley-flag-f,
  author     = {Stanley, Richard P.},
  title      = {Flag {$f$}-vectors and the {$cd$}-index},
  journal    = {Math. Z.},
  fjournal   = {Mathematische Zeitschrift},
  volume     = {216},
  year       = {1994},
  number     = {3},
  pages      = {483--499},
  issn       = {0025-5874},
  mrclass    = {06A07 (06A08 52B05 52B20)},
  mrnumber   = {1283084},
  mrreviewer = {Glenn H. Hurlbert},
  doi        = {10.1007/BF02572336},
  url        = {https://doi.org/10.1007/BF02572336}
}

@article{stanley-hyperplanes,
  author     = {Stanley, Richard p.},
  booktitle  = {Geometric {C}ombinatorics},
  doi        = {10.1090/pcms/013/08},
  mrclass    = {52C35 (05B35 55R80)},
  mrnumber   = {2383131},
  pages      = {389--496},
  publisher  = {Amer. Math. Soc., Providence, RI},
  series     = {IAS/Park City Math. Ser.},
  title      = {An {I}ntroduction to {H}yperplane {A}rrangements},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.1090/pcms/013/08},
  volume     = {13},
  year       = {2007},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.1090/pcms/013/08},
  bdsk-url-2 = {https://doi.org/10.1090/pcms/013/08}
}

@article{stanley-lattices,
  author     = {Stanley, Richard P.},
  doi        = {10.1007/BF02945028},
  fjournal   = {Algebra Universalis},
  issn       = {0002-5240},
  journal    = {Algebra Universalis},
  mrclass    = {06A20},
  mrnumber   = {309815},
  mrreviewer = {O. Frink},
  pages      = {197--217},
  title      = {Supersolvable {L}attices},
  url        = {https://doi-org.ezp3.lib.umn.edu/10.1007/BF02945028},
  volume     = {2},
  year       = {1972},
  bdsk-url-1 = {https://doi-org.ezp3.lib.umn.edu/10.1007/BF02945028},
  bdsk-url-2 = {https://doi.org/10.1007/BF02945028}
}

@article{stanley-parking,
  author     = {Stanley, Richard P.},
  doi        = {10.1073/pnas.93.6.2620},
  fjournal   = {Proceedings of the National Academy of Sciences of the United States of America},
  issn       = {0027-8424},
  journal    = {Proc. Nat. Acad. Sci. U.S.A.},
  mrclass    = {52B30 (05C30 06A06 20F55)},
  mrnumber   = {1379568},
  mrreviewer = {Hiroaki Terao},
  number     = {6},
  pages      = {2620--2625},
  title      = {Hyperplane {A}rrangements, {I}nterval {O}rders, and {T}rees},
  url        = {https://doi-org.ezp3.lib.umn.edu/10.1073/pnas.93.6.2620},
  volume     = {93},
  year       = {1996},
  bdsk-url-1 = {https://doi-org.ezp3.lib.umn.edu/10.1073/pnas.93.6.2620},
  bdsk-url-2 = {https://doi.org/10.1073/pnas.93.6.2620}
}

@book{stanley-thesis,
  author     = {Stanley, Richard P.},
  mrclass    = {05A17},
  mrnumber   = {0332509},
  mrreviewer = {L. K. Durst},
  pages      = {iii+104},
  publisher  = {American Mathematical Society, Providence, R.I.},
  series     = {Memoirs of the American Mathematical Society, No. 119},
  title      = {Ordered structures and partitions},
  year       = {1972}
}

@article{steinberg,
  author     = {Steinberg, Robert},
  doi        = {10.2307/1994152},
  fjournal   = {Transactions of the American Mathematical Society},
  issn       = {0002-9947},
  journal    = {Trans. Amer. Math. Soc.},
  mrclass    = {20.75 (14.18)},
  mrnumber   = {167535},
  mrreviewer = {J. A. Todd},
  pages      = {392--400},
  title      = {Differential {E}quations {I}nvariant under {F}inite {R}eflection {G}roups},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.2307/1994152},
  volume     = {112},
  year       = {1964},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.2307/1994152},
  bdsk-url-2 = {https://doi.org/10.2307/1994152}
}

@article{Stembridge,
  author     = {Stembridge, John R.},
  doi        = {10.1016/j.aim.2007.09.002},
  fjournal   = {Advances in Mathematics},
  issn       = {0001-8708},
  journal    = {Adv. Math.},
  mrclass    = {52B22 (06A07)},
  mrnumber   = {2388082},
  number     = {5},
  pages      = {1935--1961},
  title      = {Coxeter {C}ones and their {$h$}-vectors},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.1016/j.aim.2007.09.002},
  volume     = {217},
  year       = {2008},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.1016/j.aim.2007.09.002},
  bdsk-url-2 = {https://doi.org/10.1016/j.aim.2007.09.002}
}

@article{stembridge-p-partitions,
  author     = {Stembridge, John R.},
  title      = {Enriched {$P$}-partitions},
  journal    = {Trans. Amer. Math. Soc.},
  fjournal   = {Transactions of the American Mathematical Society},
  volume     = {349},
  year       = {1997},
  number     = {2},
  pages      = {763--788},
  issn       = {0002-9947},
  mrclass    = {06A07 (05E05 05E10)},
  mrnumber   = {1389788},
  mrreviewer = {Joseph Neggers},
  doi        = {10.1090/S0002-9947-97-01804-7},
  url        = {https://doi.org/10.1090/S0002-9947-97-01804-7}
}

@article{stump,
  author     = {Stump, Christian},
  booktitle  = {20th {A}nnual {I}nternational {C}onference on {F}ormal {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({FPSAC} 2008)},
  mrclass    = {05E15 (20F55)},
  mrnumber   = {2721462},
  mrreviewer = {Himmet Can},
  pages      = {295--306},
  publisher  = {Assoc. Discrete Math. Theor. Comput. Sci., Nancy},
  series     = {Discrete Math. Theor. Comput. Sci. Proc., AJ},
  title      = {{$q,t$}-{${\rm Fu}$}\ss -{C}atalan numbers for complex reflection groups},
  year       = {2008}
}

@book{Sturmfels,
  author     = {Sturmfels, Bernd},
  doi        = {10.1090/ulect/008},
  isbn       = {0-8218-0487-1},
  mrclass    = {13P10 (14M25 52B20)},
  mrnumber   = {1363949},
  mrreviewer = {P. Schenzel},
  pages      = {xii+162},
  publisher  = {American Mathematical Society, Providence, RI},
  series     = {University Lecture Series, Volume 8},
  title      = {Gr\"{o}bner {B}ases and {C}onvex {P}olytopes},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.1090/ulect/008},
  year       = {1996},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.1090/ulect/008},
  bdsk-url-2 = {https://doi.org/10.1090/ulect/008}
}

@article{varchenko,
  author     = {Varchenko, Alexandre},
  doi        = {10.1006/aima.1993.1003},
  fjournal   = {Advances in Mathematics},
  issn       = {0001-8708},
  journal    = {Adv. Math.},
  mrclass    = {52B30 (17B37)},
  mrnumber   = {1200291},
  mrreviewer = {Hiroaki Terao},
  number     = {1},
  pages      = {110--144},
  title      = {Bilinear {F}orm of {R}eal {C}onfiguration of {H}yperplanes},
  url        = {https://doi-org.ezp3.lib.umn.edu/10.1006/aima.1993.1003},
  volume     = {97},
  year       = {1993},
  bdsk-url-1 = {https://doi-org.ezp3.lib.umn.edu/10.1006/aima.1993.1003},
  bdsk-url-2 = {https://doi.org/10.1006/aima.1993.1003}
}

@article{VarchenkoGelfand,
  author     = {Varchenko, A. N. and Gel'fand, I. M.},
  fjournal   = {Akademiya Nauk SSSR. Funktsional' ny\u{\i} Analiz i ego Prilozheniya},
  issn       = {0374-1990},
  journal    = {Funktsional. Anal. i Prilozhen.},
  mrclass    = {32C40 (51M20)},
  mrnumber   = {925069},
  mrreviewer = {A. Verona},
  number     = {4},
  pages      = {1--18, 96},
  title      = {Heaviside {F}unctions of a {C}onfiguration of {H}yperplanes},
  volume     = {21},
  year       = {1987}
}

@article{Voll,
  author     = {Voll, Christopher},
  title      = {Functional equations for zeta functions of groups and rings},
  journal    = {Ann. of Math. (2)},
  fjournal   = {Annals of Mathematics. Second Series},
  volume     = {172},
  year       = {2010},
  number     = {2},
  pages      = {1181--1218},
  issn       = {0003-486X},
  mrclass    = {20E07 (11S40 16P90 39B52)},
  mrnumber   = {2680489},
  mrreviewer = {Alexander Fel\cprime shtyn},
  doi        = {10.4007/annals.2010.172.1185},
  url        = {https://doi.org/10.4007/annals.2010.172.1185}
}

@article{wachs,
  author        = {Michelle L. Wachs and James W. Walker},
  date-added    = {2019-02-08 10:31:52 -0600},
  date-modified = {2019-02-08 10:31:52 -0600},
  journal       = {Order},
  number        = {4},
  pages         = {367-385},
  title         = {On {G}eometric {S}emilattices},
  volume        = {2},
  year          = {1985}
}

@article{wachs-walker,
  author     = {Wachs, Michelle L. and Walker, James W.},
  doi        = {10.1007/BF00367425},
  fjournal   = {Order},
  issn       = {0167-8094},
  journal    = {Order},
  mrclass    = {06A12 (05B35 06C10)},
  mrnumber   = {838021},
  mrreviewer = {S. Rudeanu},
  number     = {4},
  pages      = {367--385},
  title      = {On geometric semilattices},
  url        = {https://doi.org/10.1007/BF00367425},
  volume     = {2},
  year       = {1986},
  bdsk-url-1 = {https://doi.org/10.1007/BF00367425}
}

@book{white,
  doi        = {10.1017/CBO9780511662041},
  editor     = {White, Neil},
  isbn       = {0-521-38165-7},
  mrclass    = {05-06},
  mrnumber   = {1165537},
  pages      = {xii+363},
  publisher  = {Cambridge University Press, Cambridge},
  series     = {Encyclopedia of Mathematics and its Applications, Volume 40},
  title      = {Matroid {A}pplications},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.1017/CBO9780511662041},
  year       = {1992},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.1017/CBO9780511662041},
  bdsk-url-2 = {https://doi.org/10.1017/CBO9780511662041}
}

@article{yuzvinsky,
  abstract   = {This is a survey of Orlik-Solomon algebras of hyperplane arrangements. These algebras first appeared in theorems due to Arnol'd, Brieskorn, and Orlik and Solomon as the cohomology algebras of the complements of complex hyperplane arrangements. Numerous applications of these algebras have subsequently been found. This survey is confined to studying Orlik-Solomon algebras per se and some of their applications to topology and combinatorics. Most of the results are taken from recent papers and preprints, although for the reader's convenience we also include relevant definitions and basic facts from the book Arrangements of hyperplanes by Orlik and Terao. For some of these facts new and more straightforward or shorter proofs are given.},
  author     = {Yuzvinsky, S.},
  doi        = {10.1070/rm2001v056n02abeh000383},
  journal    = {Russian Mathematical Surveys},
  number     = {2},
  pages      = {293--364},
  publisher  = {{IOP} Publishing},
  title      = {Orlik-Solomon algebras in algebra and topology},
  url        = {https://doi.org/10.1070/rm2001v056n02abeh000383},
  volume     = {56},
  year       = 2001,
  bdsk-url-1 = {https://doi.org/10.1070/rm2001v056n02abeh000383}
}

@article{zaslavsky-memoir,
  author     = {Zaslavsky, Thomas},
  doi        = {10.1090/memo/0154},
  fjournal   = {Memoirs of the American Mathematical Society},
  issn       = {0065-9266},
  journal    = {Mem. Amer. Math. Soc.},
  mrclass    = {05A15},
  mrnumber   = {357135},
  mrreviewer = {E. Jucovi\v{c}},
  number     = {1},
  pages      = {vii+102},
  title      = {Facing up to {A}rrangements: {F}ace-{C}ount {F}ormulas for {P}artitions of {S}pace by {H}yperplanes},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.1090/memo/0154},
  volume     = {1},
  year       = {1975},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.1090/memo/0154},
  bdsk-url-2 = {https://doi.org/10.1090/memo/0154}
}

@article{zaslavsky77,
  author     = {Zaslavsky, Thomas},
  doi        = {10.1016/0001-8708(77)90076-7},
  fjournal   = {Advances in Mathematics},
  issn       = {0001-8708},
  journal    = {Advances in Math.},
  mrclass    = {05A15 (52A25)},
  mrnumber   = {446994},
  mrreviewer = {S. F. Kapoor},
  number     = {3},
  pages      = {267--285},
  title      = {A {C}ombinatorial {A}nalysis of {T}opological {D}issections},
  url        = {https://doi.org/10.1016/0001-8708(77)90076-7},
  volume     = {25},
  year       = {1977},
  bdsk-url-1 = {https://doi.org/10.1016/0001-8708(77)90076-7}
}

@article{zaslavsky98-bib,
  author     = {Zaslavsky, Thomas},
  fjournal   = {Electronic Journal of Combinatorics},
  journal    = {Electron. J. Combin.},
  mrclass    = {05-00 (00A15 05C22)},
  mrnumber   = {1744869},
  note       = {Manuscript prepared with Marge Pratt},
  pages      = {Dynamic Surveys 8, 124},
  title      = {A {M}athematical {B}ibliography of {S}igned and {G}ain {G}raphs and {A}llied {A}reas},
  url        = {http://www.combinatorics.org/Surveys/index.html},
  volume     = {5},
  year       = {1998},
  bdsk-url-1 = {http://www.combinatorics.org/Surveys/index.html}
}

@book{ziegler,
  author     = {Ziegler, G\"{u}nter M.},
  doi        = {10.1007/978-1-4613-8431-1},
  isbn       = {0-387-94365-X},
  mrclass    = {52Bxx},
  mrnumber   = {1311028},
  mrreviewer = {Margaret M. Bayer},
  pages      = {x+370},
  publisher  = {Springer-Verlag, New York},
  series     = {Graduate Texts in Mathematics, Volume 152},
  title      = {Lectures on {P}olytopes},
  url        = {https://doi-org.ezp2.lib.umn.edu/10.1007/978-1-4613-8431-1},
  year       = {1995},
  bdsk-url-1 = {https://doi-org.ezp2.lib.umn.edu/10.1007/978-1-4613-8431-1},
  bdsk-url-2 = {https://doi.org/10.1007/978-1-4613-8431-1}
}

@article{ziegler-nonorientable,
  author     = {Ziegler, G\"{u}nter M.},
  title      = {Some minimal nonorientable matroids of rank three},
  journal    = {Geom. Dedicata},
  fjournal   = {Geometriae Dedicata},
  volume     = {38},
  year       = {1991},
  number     = {3},
  pages      = {365--371},
  issn       = {0046-5755,1572-9168},
  mrclass    = {05B35},
  mrnumber   = {1112674},
  mrreviewer = {Neil\ L.\ White},
  doi        = {10.1007/BF00181199},
  url        = {https://doi.org/10.1007/BF00181199}
}


@article{ziegler-shellability,
  author     = {Ziegler, G\"{u}nter M.},
  doi        = {10.1023/A:1022492019120},
  fjournal   = {Journal of Algebraic Combinatorics. An International Journal},
  issn       = {0925-9899},
  journal    = {J. Algebraic Combin.},
  mrclass    = {52B40 (05B25 05B35 52B30)},
  mrnumber   = {1194080},
  mrreviewer = {Michel Yves Jambu},
  number     = {3},
  pages      = {283--300},
  title      = {Matroid shellability, {$\beta$}-systems, and affine hyperplane arrangements},
  url        = {https://doi.org/10.1023/A:1022492019120},
  volume     = {1},
  year       = {1992},
  bdsk-url-1 = {https://doi.org/10.1023/A:1022492019120}
}