@misc{MV2arxiv,
      title={Hall-Littlewood polynomials, affine Schubert series, and lattice enumeration}, 
      author={J. Maglione and C. Voll},
      year={2024},
      eprinttype={arXiv},
      primaryClass={math.CO},
      eprint = {2410.08075}, 
}

@article {duSL/96,
    AUTHOR = {M. P. F. du Marcus and A. Lubotzky},
     TITLE = {Functional equations and uniformity for local zeta functions
              of nilpotent groups},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {118},
      YEAR = {1996},
    NUMBER = {1},
     PAGES = {39--90}}

@manual{Zeta,
        author= "T. Rossmann",
        title = "{\textsf{\textup{Zeta}}, ver.\ 0.4}",
        year  = 2019,
        note  = "See \url{http://www.maths.nuigalway.ie/~rossmann/Zeta/}.",
} 

@article {Rossmann/15,
    AUTHOR = {T. Rossmann},
     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}}

@article {duSG/00,
    AUTHOR = {M. P. F. {du Sautoy} and F. Grunewald},
     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},
       DOI = {10.2307/2661355},
       }

@article {Solomon/77,
    AUTHOR = {L. Solomon},
     TITLE = {Zeta functions and integral representation theory},
   JOURNAL = {Advances in Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {26},
      YEAR = {1977},
    NUMBER = {3},
     PAGES = {306--326},
       DOI = {10.1016/0001-8708(77)90044-5},
       }

@book {BS/18,
    AUTHOR = {M. Beck and R. Sanyal},
     TITLE = {Combinatorial reciprocity theorems},
    SERIES = {Graduate Studies in Mathematics},
    VOLUME = {195},
      NOTE = {An invitation to enumerative geometric combinatorics},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {2018},
     PAGES = {xiv+308 pp.}}

@article {BumpNakasuji/10,
    AUTHOR = {D. Bump and M. Nakasuji},
     TITLE = {Integration on {$p$}-adic groups and crystal bases},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {138},
      YEAR = {2010},
    NUMBER = {5},
     PAGES = {1595--1605}}

@article {Gale/68,
    AUTHOR = {Gale, David},
     TITLE = {Optimal assignments in an ordered set: {A}n application of
              matroid theory},
   JOURNAL = {J. Combinatorial Theory},
  FJOURNAL = {Journal of Combinatorial Theory},
    VOLUME = {4},
      YEAR = {1968},
     PAGES = {176--180},
   MRCLASS = {05.35 (90.00)},
  MRNUMBER = {227039},
MRREVIEWER = {A.\ Lehman},
}

@article {Vince/00,
    AUTHOR = {Vince, A.},
     TITLE = {The greedy algorithm and {C}oxeter matroids},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {11},
      YEAR = {2000},
    NUMBER = {2},
     PAGES = {155--178},
   MRCLASS = {05B35 (05E15 20F55)},
  MRNUMBER = {1761912},
MRREVIEWER = {Joseph\ Kung},
       DOI = {10.1023/A:1008780132748},
}

@book {Fulton/97,
    AUTHOR = {Fulton, William},
     TITLE = {Young tableaux},
    SERIES = {London Mathematical Society Student Texts},
    VOLUME = {35},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {1997},
     PAGES = {x+260}}

@article {SV2,
    AUTHOR = {Schein, Michael M. and Voll, Christopher},
     TITLE = {Normal zeta functions of the {H}eisenberg groups over number
              rings {II}---the non-split case},
   JOURNAL = {Israel J. Math.},
  FJOURNAL = {Israel Journal of Mathematics},
    VOLUME = {211},
      YEAR = {2016},
    NUMBER = {1},
     PAGES = {171--195}}

@article {GSS/88,
    AUTHOR = {Grunewald, F. J. and Segal, D. and Smith, G. C.},
     TITLE = {Subgroups of finite index in nilpotent groups},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {93},
      YEAR = {1988},
    NUMBER = {1},
     PAGES = {185--223},
   MRCLASS = {11M41 (03C10 03C60 20F18)},
  MRNUMBER = {943928},
MRREVIEWER = {Daniel\ Barsky},
       DOI = {10.1007/BF01393692},
}

@misc{OEIS:A003121,
  author    = {N. J. A. Sloane},
  title     = {{OEIS Sequence A003121}},
  year      = 2021,
  url       = {https://oeis.org/A003121},
  note      = {Accessed: 2024-10-03}  
} 

@misc{OEIS:A005118,
  author    = {N. J. A. Sloane},
  title     = {{OEIS Sequence A005118}},
  year      = 2021,
  url       = {https://oeis.org/A003121},
  note      = {Accessed: 2024-10-03}  
} 

@article {Voll/04,
    AUTHOR = {Voll, Christopher},
     TITLE = {Zeta functions of groups and enumeration in {B}ruhat-{T}its
              buildings},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {126},
      YEAR = {2004},
    NUMBER = {5},
     PAGES = {1005--1032},
     doi = {10.1353/ajm.2004.0041}
     }

@article {StasinskiVoll/13,
    AUTHOR = {Stasinski, Alexander and Voll, Christopher},
     TITLE = {A new statistic on the hyperoctahedral groups},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {20},
      YEAR = {2013},
    NUMBER = {3},
     PAGES = {Paper 50, 23 pp.}}

@article {Satake/63,
    AUTHOR = {Satake, Ichir\^{o}},
     TITLE = {Theory of spherical functions on reductive algebraic groups
              over {$p$}-adic fields},
   JOURNAL = {Inst. Hautes \'{E}tudes Sci. Publ. Math.},
  FJOURNAL = {Institut des Hautes \'{E}tudes Scientifiques. Publications
              Math\'{e}matiques},
      YEAR = {1963},
    NUMBER = {18},
     PAGES = {5--69}}

@incollection {Voll/11,
    AUTHOR = {Voll, Christopher},
     TITLE = {A newcomer's guide to zeta functions of groups and rings},
 BOOKTITLE = {Lectures on profinite topics in group theory},
    SERIES = {London Math. Soc. Stud. Texts},
    VOLUME = {77},
     PAGES = {99--144},
 PUBLISHER = {Cambridge Univ. Press, Cambridge},
      YEAR = {2011},
      doi = {10.1017/CBO9780511793837.005}
      }

@misc{Woodcock,
  Author={Woodcock, Jennifer},
  Title={Properties of the poset of {D}yck paths ordered by inclusion},
  Year={2008},
  Note={\href{https://arxiv.org/abs/1011.5008}{\texttt{arXiv:1011.5008}}},
}

@article {FM/16,
    AUTHOR = {Feigin, Boris and Makhlin, Igor},
     TITLE = {A combinatorial formula for affine {H}all--{L}ittlewood
              functions via a weighted {B}rion theorem},
   JOURNAL = {Selecta Math. (N.S.)},
  FJOURNAL = {Selecta Mathematica. New Series},
    VOLUME = {22},
      YEAR = {2016},
    NUMBER = {3},
     PAGES = {1703--1747},
       DOI = {10.1007/s00029-016-0223-4},
       }

@article {BGS/22,
    AUTHOR = {Berman, Mark N. and Glazer, Itay and Schein, Michael M.},
     TITLE = {Pro-isomorphic zeta functions of nilpotent groups and {L}ie
              rings under base extension},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {375},
      YEAR = {2022},
    NUMBER = {2},
     PAGES = {1051--1100},
       DOI = {10.1090/tran/8506},}

@article {BW:Bruhat,
    AUTHOR = {Bj\"orner, Anders and Wachs, Michelle},
     TITLE = {Bruhat order of {C}oxeter groups and shellability},
   JOURNAL = {Adv. in Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {43},
      YEAR = {1982},
    NUMBER = {1},
     PAGES = {87--100},
   MRCLASS = {20H15 (06A10 13F20 14L30 52A43)},
  MRNUMBER = {644668},
MRREVIEWER = {S.\ Milne},
       DOI = {10.1016/0001-8708(82)90029-9},
       URL = {https://doi.org/10.1016/0001-8708(82)90029-9},
}

@article {Petrogradsky/07,
    AUTHOR = {Petrogradsky, V. M.},
     TITLE = {Multiple zeta functions and asymptotic structure of free
              abelian groups of finite rank},
   JOURNAL = {J. Pure Appl. Algebra},
  FJOURNAL = {Journal of Pure and Applied Algebra},
    VOLUME = {208},
      YEAR = {2007},
    NUMBER = {3},
     PAGES = {1137--1158}}

@article {BushnellReiner/80,
    AUTHOR = {Bushnell, Colin J. and Reiner, Irving},
     TITLE = {Zeta functions of arithmetic orders and {S}olomon's
              conjectures},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {173},
      YEAR = {1980},
    NUMBER = {2},
     PAGES = {135--161},
       DOI = {10.1007/BF01159955},
       }

@book {LubotzkySegal/03,
    AUTHOR = {Lubotzky, Alexander and Segal, Dan},
     TITLE = {Subgroup growth},
    SERIES = {Progress in Mathematics},
    VOLUME = {212},
 PUBLISHER = {Birkh\"auser Verlag, Basel},
      YEAR = {2003},
     PAGES = {xxii+453 pp.}, 
       DOI = {10.1007/978-3-0348-8965-0},
       URL = {https://doi.org/10.1007/978-3-0348-8965-0},
}

@article {Igusa/89,
    AUTHOR = {Igusa, Jun-ichi},
     TITLE = {Universal {$p$}-adic zeta functions and their functional
              equations},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {111},
      YEAR = {1989},
    NUMBER = {5},
     PAGES = {671--716}}

@article {LV/23,
    AUTHOR = {Lee, Seungjai and Voll, Christopher},
     TITLE = {Zeta functions of integral nilpotent quiver representations},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2023},
    NUMBER = {4},
     PAGES = {3460--3515},
       DOI = {10.1093/imrn/rnab345},
       }

@article {CSV/24,
    AUTHOR = {Carnevale, Angela and Schein, Michael M. and Voll,
              Christopher},
     TITLE = {Generalized {I}gusa functions and ideal growth in nilpotent
              {L}ie rings},
   JOURNAL = {Algebra Number Theory},
  FJOURNAL = {Algebra \& Number Theory},
    VOLUME = {18},
      YEAR = {2024},
    NUMBER = {3},
     PAGES = {537--582}}


@article {Thrall/52,
    AUTHOR = {Thrall, R. M.},
     TITLE = {A combinatorial problem},
   JOURNAL = {Michigan Math. J.},
  FJOURNAL = {Michigan Mathematical Journal},
    VOLUME = {1},
      YEAR = {1952},
     PAGES = {81--88}}


@article {CSV/20,
    AUTHOR = {Carnevale, Angela and Schein, Michael M. and Voll,
              Christopher},
     TITLE = {Generalized {I}gusa functions and ideal growth in nilpotent
              {L}ie rings},
   JOURNAL = {S\'{e}m. Lothar. Combin.},
  FJOURNAL = {S\'{e}minaire Lotharingien de Combinatoire},
    VOLUME = {84B},
      YEAR = {2020},
     PAGES = {Art. 71, 12 pp.}}

@article {KL/72,
    AUTHOR = {Kleiman, S. L. and Laksov, Dan},
     TITLE = {Schubert calculus},
   JOURNAL = {Amer. Math. Monthly},
  FJOURNAL = {American Mathematical Monthly},
    VOLUME = {79},
      YEAR = {1972},
     PAGES = {1061--1082},
       DOI = {10.2307/2317421},
       }

@book {Cohen,
    AUTHOR = {Cohen, Henri},
     TITLE = {Advanced topics in computational number theory},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {193},
 PUBLISHER = {Springer-Verlag, New York},
      YEAR = {2000},
     PAGES = {xvi+578 pp.},
   MRCLASS = {11Y40 (11Rxx)},
  MRNUMBER = {1728313},
MRREVIEWER = {Ken\ Yamamura},
       DOI = {10.1007/978-1-4419-8489-0},
       URL = {https://doi.org/10.1007/978-1-4419-8489-0},
}

@misc{AMV1/24,
    author = {Alfes, Claudia and Maglione, Joshua and Voll, Christopher},
    title = {{Enumerating lattices by Schubert--Smith parameters}},
}

@article {AMV2/24,
    AUTHOR = {Alfes, Claudia and Maglione, Joshua and Voll, Christopher},
     TITLE = {{Ehrhart polynomials, Hecke series, and affine buildings}},
   JOURNAL = {S\'em. Lothar. Combin.},
  FJOURNAL = {S\'eminaire Lotharingien de Combinatoire},
    VOLUME = {91B},
      YEAR = {2024},
     PAGES = {Art. 84, pp.~12},
}

@misc{MV/21, 
    author = {Maglione, Joshua and Voll, Christopher},
    keywords = {Combinatorics (math.CO), Algebraic Geometry (math.AG), Number Theory (math.NT), FOS: Mathematics, FOS: Mathematics},
    title = {{Flag Hilbert--Poincar\'e series of hyperplane arrangements and
                  their Igusa zeta functions}},
   year =     {2021},
   eprinttype = {arXiv},
   eprint = {2103.03640},
   note = {To appear in Israel J.\ Math. }
   }


@article {CSV/18,
    AUTHOR = {Carnevale, Angela and Shechter, Shai and Voll, Christopher},
     TITLE = {Enumerating traceless matrices over compact discrete valuation
              rings},
   JOURNAL = {Israel J. Math.},
  FJOURNAL = {Israel Journal of Mathematics},
    VOLUME = {227},
      YEAR = {2018},
    NUMBER = {2},
     PAGES = {957--986},
   MRCLASS = {15B33 (05E15 13G05 13P25 20F55)},
  MRNUMBER = {3846349},
MRREVIEWER = {Yijia Tan},
       DOI = {10.1007/s11856-018-1755-4},
       URL = {https://doi.org/10.1007/s11856-018-1755-4},
}

@book {Humphreys/90,
    AUTHOR = {Humphreys, James E.},
     TITLE = {Reflection groups and {C}oxeter groups},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {29},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {1990},
     PAGES = {xii+204 pp.},
   MRCLASS = {20-02 (20F32 20F55 20G15 20H15)},
  MRNUMBER = {1066460},
MRREVIEWER = {Louis Solomon},
       DOI = {10.1017/CBO9780511623646},
       URL = {https://doi.org/10.1017/CBO9780511623646},
}

@article {Reiner/93,
    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},
   MRCLASS = {05A15 (05E05)},
  MRNUMBER = {1248063},
MRREVIEWER = {Edward E. Allen},
       DOI = {10.1006/eujc.1993.1058},
       URL = {https://doi.org/10.1006/eujc.1993.1058},
}
@book {Macdonald/95,
    AUTHOR = {Macdonald, I. G.},
     TITLE = {Symmetric functions and {H}all polynomials},
    SERIES = {Oxford Mathematical Monographs},
   EDITION = {Second},
 PUBLISHER = {The Clarendon Press, Oxford University Press, New York},
      YEAR = 1995,
     PAGES = {x+475 pp.},
   MRCLASS = {05E05 (05-02 20C30 20C33 20K01 33C80 33D80)},
  MRNUMBER = 1354144,
MRREVIEWER = {John R. Stembridge},
}

@article {Tamagawa/63,
    AUTHOR = {Tamagawa, Tsuneo},
     TITLE = {On the {$\zeta $}-functions of a division algebra},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = 77,
      YEAR = 1963,
     PAGES = {387--405},
   MRCLASS = {10.66 (10.41)},
  MRNUMBER = 144928,
MRREVIEWER = {K. Iwasawa},
       DOI = {10.2307/1970221},
       URL = {https://doi.org/10.2307/1970221},
}


		  
@book {Andrianov/87,
    AUTHOR = {Andrianov, Anatolij N.},
     TITLE = {Quadratic forms and {H}ecke operators},
    SERIES = {Grundlehren der mathematischen Wissenschaften [Fundamental
              Principles of Mathematical Sciences]},
    VOLUME = {286},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {1987},
     PAGES = {xii+374},
   MRCLASS = {11F46 (11E45)},
  MRNUMBER = {884891},
MRREVIEWER = {Harvey Cohn},
       DOI = {10.1007/978-3-642-70341-6},
       URL = {https://doi.org/10.1007/978-3-642-70341-6},
}
 
@article {Andrianov/69,
    AUTHOR = {Andrianov, A. N.},
     TITLE = {Rationality theorems for {H}ecke series and {Z}eta functions
              of the groups {${\rm GL}\sb{n}$} and {${\rm Sp}\sb{n}$} over
              local fields},
   JOURNAL = {Izv. Akad. Nauk SSSR Ser. Mat.},
  FJOURNAL = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya},
      YEAR = {1969},
     PAGES = {466--505},
   MRCLASS = {10.21},
  MRNUMBER = {262168},
MRREVIEWER = {K.-B.\ Gundlach},
}

@article {PanchishkinVankov/07,
    AUTHOR = {Panchishkin, Alexei and Vankov, Kirill},
     TITLE = {Explicit {S}himura's conjecture for {${\rm Sp}_3$} on a
              computer},
   JOURNAL = {Math. Res. Lett.},
  FJOURNAL = {Mathematical Research Letters},
    VOLUME = {14},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {173--187},
   MRCLASS = {11F25 (11M41)},
  MRNUMBER = {2318617},
       DOI = {10.4310/MRL.2007.v14.n2.a2},
}

@article {Vankov/11,
    AUTHOR = {Vankov, Kirill},
     TITLE = {Explicit {H}ecke series for symplectic group of genus 4},
   JOURNAL = {J. Th\'{e}or. Nombres Bordeaux},
  FJOURNAL = {Journal de Th\'{e}orie des Nombres de Bordeaux},
    VOLUME = {23},
      YEAR = {2011},
    NUMBER = {1},
     PAGES = {279--298},
   MRCLASS = {11F60},
  MRNUMBER = {2780630},
MRREVIEWER = {Hidenori\ Katsurada},
       DOI = {10.5802/jtnb.761},
}

@book {Garrett,
    AUTHOR = {Garrett, Paul},
     TITLE = {Buildings and classical groups},
 PUBLISHER = {Chapman \& Hall, London},
      YEAR = {1997},
     PAGES = {xii+373},
   MRCLASS = {20G25 (20E42 51E24)},
  MRNUMBER = {1449872},
MRREVIEWER = {Herbert Abels},
       DOI = {10.1007/978-94-011-5340-9},
       URL = {https://doi.org/10.1007/978-94-011-5340-9},
}

@book {Wan/93,
    AUTHOR = {Wan, Zhe Xian},
     TITLE = {Geometry of classical groups over finite fields},
 PUBLISHER = {Studentlitteratur, Lund; Chartwell-Bratt Ltd., Bromley},
      YEAR = {1993},
     PAGES = {viii+394}}

@article {StasinskiVoll/14,
    AUTHOR = {Stasinski, A. and Voll, C.},
     TITLE = {Representation zeta functions of nilpotent groups and
              generating functions for {W}eyl groups of type {$B$}},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {136},
      YEAR = {2014},
    NUMBER = {2},
     PAGES = {501--550}}

@article {Boecherer/86,
    AUTHOR = {B\"{o}cherer, S.},
     TITLE = {Ein {R}ationalit\"{a}tssatz f\"{u}r formale {H}eckereihen zur
              {S}iegelschen {M}odulgruppe},
   JOURNAL = {Abh. Math. Sem. Univ. Hamburg},
  FJOURNAL = {Abhandlungen aus dem Mathematischen Seminar der Universit\"{a}t
              Hamburg},
    VOLUME = {56},
      YEAR = {1986},
     PAGES = {35--47}}

@article {Krieg/90,
    AUTHOR = {Krieg, Aloys},
     TITLE = {Hecke algebras},
   JOURNAL = {Mem. Amer. Math. Soc.},
  FJOURNAL = {Memoirs of the American Mathematical Society},
    VOLUME = {87},
      YEAR = {1990},
    NUMBER = {435},
     PAGES = {x+158}}

@article {GRV/07,
    AUTHOR = {Gunnells, Paul E. and Rodriguez Villegas, Fernando},
     TITLE = {Lattice polytopes, {H}ecke operators, and the {E}hrhart
              polynomial},
   JOURNAL = {Selecta Math. (N.S.)},
  FJOURNAL = {Selecta Mathematica. New Series},
    VOLUME = {13},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {253--276}}

@inbook{cayley_2009, place={Cambridge}, series={Cambridge Library Collection - Mathematics}, title={On the Analytical Forms called Trees. Second Part}, volume={4}, DOI={10.1017/CBO9780511703706.026}, booktitle={The Collected Mathematical Papers}, publisher={Cambridge University Press}, author={Cayley, Arthur}, year={2009}, pages={112-115}, collection={Cambridge Library Collection - Mathematics}}

@book {Knuth/94,
    AUTHOR = {Graham, Ronald L. and Knuth, Donald E. and Patashnik, Oren},
     TITLE = {Concrete mathematics},
   EDITION = {Second},
 PUBLISHER = {Addison-Wesley Publishing Company, Reading, MA},
      YEAR = {1994},
     PAGES = {xiv+657},
   MRCLASS = {68-01 (00-01 00A05 05-01 68Rxx)},
  MRNUMBER = {1397498},
MRREVIEWER = {Volker Strehl},
}

@misc{Wu/20,
      title={{B}ernstein-{S}ato ideals and hyperplane arrangements}, 
      author={Lei Wu},
      year={2020},
     note={\texttt{\href{https://arxiv.org/abs/2005.13502}{arXiv:2005.13502}}},
      eprint={2005.13502},
      archivePrefix={arXiv},
      primaryClass={math.AG}
}

@article {CluckersLoeser/10,
    AUTHOR = {Cluckers, Raf and Loeser, Fran\c{c}ois},
     TITLE = {Constructible exponential functions, motivic {F}ourier
              transform and transfer principle},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {171},
      YEAR = {2010},
    NUMBER = {2},
     PAGES = {1011--1065},
   MRCLASS = {14E18},
  MRNUMBER = {2630060},
MRREVIEWER = {Tommaso De Fernex},
       DOI = {10.4007/annals.2010.171.1011},
       URL = {https://doi.org/10.4007/annals.2010.171.1011},
}

@article {Hu/03,
    AUTHOR = {Hu, Yi},
     TITLE = {A compactification of open varieties},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {355},
      YEAR = {2003},
    NUMBER = {12},
     PAGES = {4737--4753},
   MRCLASS = {14N20 (14C05)},
  MRNUMBER = {1997581},
MRREVIEWER = {G. K. Sankaran},
       DOI = {10.1090/S0002-9947-03-03247-1},
       URL = {https://doi.org/10.1090/S0002-9947-03-03247-1},
}

@article {Rossmann/18,
    AUTHOR = {Rossmann, Tobias},
     TITLE = {Computing local zeta functions of groups, algebras, and
              modules},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {370},
      YEAR = {2018},
    NUMBER = {7},
     PAGES = {4841--4879},
   MRCLASS = {11M41 (20C15 20F18 20F69 20G30)},
  MRNUMBER = {3812098},
MRREVIEWER = {Asif\ Zaman},
       DOI = {10.1090/tran/7361},
}


@misc{budur2020contact,
      title={On contact loci of hyperplane arrangements}, 
      author={Nero Budur and Tran Quang Tue},
      year={2020},
      note={\texttt{\href{https://arxiv.org/abs/2002.08480}{arXiv:2002.08480}}},
      archivePrefix={arXiv},
      primaryClass={math.AG}
}

@book {Comtet/74,
    AUTHOR = {Comtet, Louis},
     TITLE = {Advanced combinatorics},
   EDITION = {enlarged},
      NOTE = {The art of finite and infinite expansions},
 PUBLISHER = {D. Reidel Publishing Co., Dordrecht},
      YEAR = {1974},
     PAGES = {xi+343},
   MRCLASS = {05-02},
  MRNUMBER = {0460128},
}

@article {Stanley/78,
    AUTHOR = {Stanley, Richard P.},
     TITLE = {Hilbert functions of graded algebras},
   JOURNAL = {Advances in Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {28},
      YEAR = {1978},
    NUMBER = {1},
     PAGES = {57--83},
   MRCLASS = {13D10 (13H10)},
  MRNUMBER = {485835},
MRREVIEWER = {Idun Reiten},
       DOI = {10.1016/0001-8708(78)90045-2},
       URL = {https://doi.org/10.1016/0001-8708(78)90045-2},
}

@book {Petersen/15,
    AUTHOR = {Petersen, T. Kyle},
     TITLE = {Eulerian numbers},
    SERIES = {Birkh\"{a}user Advanced Texts: Basler Lehrb\"{u}cher},
 PUBLISHER = {Birkh\"{a}user/Springer, New York},
      YEAR = 2015,
     PAGES = {xviii+456},
      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},
       DOI = {10.1007/978-1-4939-3091-3},
       URL = {https://doi.org/10.1007/978-1-4939-3091-3},
}

@article {SV1/15,
    AUTHOR = {Schein, Michael M. and Voll, Christopher},
     TITLE = {Normal zeta functions of the {H}eisenberg groups over number
              rings~{I}: the unramified case},
   JOURNAL = {J. Lond. Math. Soc. (2)},
  FJOURNAL = {Journal of the London Mathematical Society. Second Series},
    VOLUME = {91},
      YEAR = {2015},
    NUMBER = {1},
     PAGES = {19--46},
   MRCLASS = {20E07 (05A10 11M41)},
  MRNUMBER = {3338607},
MRREVIEWER = {Sandro Bettin},
       DOI = {10.1112/jlms/jdu061},
       URL = {https://doi.org/10.1112/jlms/jdu061},
}

@article {Voll/19,
    AUTHOR = {Voll, Christopher},
     TITLE = {Local functional equations for submodule zeta functions
              associated to nilpotent algebras of endomorphisms},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2019},
    NUMBER = {7},
     PAGES = {2137--2176},
   MRCLASS = {11M41 (11S40 16W20 20E07)},
  MRNUMBER = {3938319},
MRREVIEWER = {Shin-ya Koyama},
}

@article {Voll/10,
    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},
   MRCLASS = {20E07 (11S40 16P90 39B52)},
  MRNUMBER = {2680489},
MRREVIEWER = {Alexander Fel\cprime shtyn},
       DOI = {10.4007/annals.2010.172.1185},
}

@book {BjoernerBrenti/05,
    AUTHOR = {Bj\"{o}rner, Anders and Brenti, Francesco},
     TITLE = {Combinatorics of {C}oxeter groups},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {231},
 PUBLISHER = {Springer, New York},
      YEAR = {2005},
     PAGES = {xiv+363},
      ISBN = {978-3540-442387; 3-540-44238-3},
   MRCLASS = {05-01 (05E15 20F55)},
  MRNUMBER = {2133266},
MRREVIEWER = {Jian-yi Shi},
}

@article {Bjoerner:NBC,
    AUTHOR = {Bj\"{o}rner, Anders},
     TITLE = {On the homology of geometric lattices},
   JOURNAL = {Algebra Universalis},
  FJOURNAL = {Algebra Universalis},
    VOLUME = {14},
      YEAR = {1982},
    NUMBER = {1},
     PAGES = {107--128},
   MRCLASS = {05B35 (06C10 57M15)},
  MRNUMBER = {634422},
MRREVIEWER = {Louis Solomon},
       DOI = {10.1007/BF02483913},
       URL = {https://doi.org/10.1007/BF02483913},
}

@article {VeysZunigaGalindo/08,
    AUTHOR = {Veys, Willem and Z\'{u}\~{n}iga-Galindo, W. A.},
     TITLE = {Zeta functions for analytic mappings, log-principalization of
              ideals, and {N}ewton polyhedra},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {360},
      YEAR = {2008},
    NUMBER = {4},
     PAGES = {2205--2227},
   MRCLASS = {11S40 (11D79 14M25)},
  MRNUMBER = {2366980},
MRREVIEWER = {Jerzy Browkin},
       DOI = {10.1090/S0002-9947-07-04422-4},
       URL = {https://doi.org/10.1090/S0002-9947-07-04422-4},
}

@article {BW:partition-lattices,
    AUTHOR = {Bj\"{o}rner, Anders and Wachs, Michelle L.},
     TITLE = {Geometrically constructed bases for homology of partition
              lattices of type {$A$}, {$B$} and {$D$}},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {11},
      YEAR = {2004/06},
    NUMBER = {2},
     PAGES = {Research Paper 3, 26},
   MRCLASS = {52C35 (05E25)},
  MRNUMBER = {2120098},
MRREVIEWER = {Daniel C. Cohen},
       URL = {http://www.combinatorics.org/Volume_11/Abstracts/v11i2r3.html},
}

@incollection {Wachs/07,
    AUTHOR = {Wachs, Michelle L.},
     TITLE = {Poset topology: tools and applications},
 BOOKTITLE = {Geometric combinatorics},
    SERIES = {IAS/Park City Math. Ser.},
    VOLUME = {13},
     PAGES = {497--615},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2007},
   MRCLASS = {06B30 (05E10 52C35 55R80)},
  MRNUMBER = {2383132},
       DOI = {10.1090/pcms/013/09},
       URL = {https://doi.org/10.1090/pcms/013/09},
}

@manual{OEIS,
author = {{OEIS Foundation Inc.}},
year = {2020},
title = {The {O}n-{L}ine {E}ncyclopedia of {I}nteger {S}equences},
NOTE = {\url{http://oeis.org/}},
}


@MISC{oeis/ultradissim,
  AUTHOR       = "OEIS Foundation Inc. (2020)",
  TITLE        = "The On-Line Encyclopedia of Integer Sequences",
  YEAR         = "2020",
  NOTE         = "\url{http://oeis.org/A005121}"
}


@MISC{oeis/schroeder4-unlab,
  AUTHOR       = "OEIS Foundation Inc. (2020)",
  TITLE        = "The On-Line Encyclopedia of Integer Sequences",
  YEAR         = "2020",
  NOTE         = "\url{http://oeis.org/A000699}"
}


@MISC{oeis/schroeder4,
  AUTHOR       = "OEIS Foundation Inc. (2020)",
  TITLE        = "The On-Line Encyclopedia of Integer Sequences",
  YEAR         = "2020",
  NOTE         = "\url{http://oeis.org/A000311}"
}

@book {OrlikTerao/92,
    AUTHOR = {Orlik, Peter and Terao, Hiroaki},
     TITLE = {Arrangements of hyperplanes},
    SERIES = {Grundlehren der Mathematischen Wissenschaften [Fundamental
              Principles of Mathematical Sciences]},
    VOLUME = {300},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {1992},
     PAGES = {xviii+325},
   MRCLASS = {52B30 (14F35 20F36 20F55 32S25 57N65)},
  MRNUMBER = {1217488},
MRREVIEWER = {Michel Yves Jambu},
       DOI = {10.1007/978-3-662-02772-1},
       URL = {https://doi.org/10.1007/978-3-662-02772-1},
}

@incollection {Stanley/07,
    AUTHOR = {Stanley, Richard P.},
     TITLE = {An introduction to hyperplane arrangements},
 BOOKTITLE = {Geometric combinatorics},
    SERIES = {IAS/Park City Math. Ser.},
    VOLUME = {13},
     PAGES = {389--496},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2007},
   MRCLASS = {52C35 (05B35 55R80)},
  MRNUMBER = {2383131},
       DOI = {10.1090/pcms/013/08},
       URL = {https://doi.org/10.1090/pcms/013/08},
}

@article {Armstrong:noncrossing-partitions,
    AUTHOR = {Armstrong, Drew},
     TITLE = {Generalized noncrossing partitions and combinatorics of
              {C}oxeter groups},
   JOURNAL = {Mem. Amer. Math. Soc.},
  FJOURNAL = {Memoirs of the American Mathematical Society},
    VOLUME = {202},
      YEAR = {2009},
    NUMBER = {949},
     PAGES = {x+159},
   MRCLASS = {05-02 (05A17 05E15 05E18 06A06 20F55)},
  MRNUMBER = {2561274},
       DOI = {10.1090/S0065-9266-09-00565-1},
       URL = {https://doi.org/10.1090/S0065-9266-09-00565-1},
}

@article {BW:Weyl-monodromy,
    AUTHOR = {Bapat, Asilata and Walters, Robin},
     TITLE = {The strong topological monodromy conjecture for {W}eyl
              hyperplane arrangements},
   JOURNAL = {Math. Res. Lett.},
  FJOURNAL = {Mathematical Research Letters},
    VOLUME = {24},
      YEAR = {2017},
    NUMBER = {4},
     PAGES = {947--954},
   MRCLASS = {32S22 (17B22)},
  MRNUMBER = {3723798},
MRREVIEWER = {Shaheen Nazir},
       DOI = {10.4310/MRL.2017.v24.n4.a1},
       URL = {https://doi.org/10.4310/MRL.2017.v24.n4.a1},
}

@article {BW:generalized-quotients,
    AUTHOR = {Bj\"{o}rner, Anders and Wachs, Michelle L.},
     TITLE = {Generalized quotients in {C}oxeter groups},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {308},
      YEAR = {1988},
    NUMBER = {1},
     PAGES = {1--37},
   MRCLASS = {05A99 (06F99 20B30 20F99)},
  MRNUMBER = {946427},
MRREVIEWER = {Joseph Kung},
       DOI = {10.2307/2000946},
       URL = {https://doi.org/10.2307/2000946},
}

@inproceedings {BW:Artin-groups,
    AUTHOR = {Brady, Thomas and Watt, Colum},
     TITLE = {{$K(\pi,1)$}'s for {A}rtin groups of finite type},
 BOOKTITLE = {Proceedings of the {C}onference on {G}eometric and
              {C}ombinatorial {G}roup {T}heory, {P}art {I} ({H}aifa, 2000)},
   JOURNAL = {Geom. Dedicata},
  FJOURNAL = {Geometriae Dedicata},
    VOLUME = {94},
      YEAR = {2002},
     PAGES = {225--250},
   MRCLASS = {20F36 (05E15 06A07 20F55)},
  MRNUMBER = {1950880},
       DOI = {10.1023/A:1020902610809},
       URL = {https://doi.org/10.1023/A:1020902610809},
}

@article {BMT:Monodromy,
    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},
   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},
}

@article {BSY:zeta-b-functions,
    AUTHOR = {Budur, Nero and Saito, Morihiko and Yuzvinsky, Sergey},
     TITLE = {On the local zeta functions and the {$b$}-functions of certain
              hyperplane arrangements},
      NOTE = {With an appendix by Willem Veys},
   JOURNAL = {J. Lond. Math. Soc. (2)},
  FJOURNAL = {Journal of the London Mathematical Society. Second Series},
    VOLUME = {84},
      YEAR = {2011},
    NUMBER = {3},
     PAGES = {631--648},
   MRCLASS = {11S40 (14F10 32S22 32S40)},
  MRNUMBER = {2855794},
MRREVIEWER = {Margaret M. Robinson},
       DOI = {10.1112/jlms/jdr025},
       URL = {https://doi.org/10.1112/jlms/jdr025},
}

@incollection {Denef:Report,
    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 (1992)},
   MRCLASS = {11S40 (14G20)},
  MRNUMBER = {1157848},
MRREVIEWER = {Boris Datskovsky},
}

@article {DL:top-zf,
    AUTHOR = {Denef, J. and Loeser, F.},
     TITLE = {Caract\'{e}ristiques d'{E}uler-{P}oincar\'{e}, fonctions z\^{e}ta locales
              et modifications analytiques},
   JOURNAL = {J. Amer. Math. Soc.},
  FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {5},
      YEAR = {1992},
    NUMBER = {4},
     PAGES = {705--720},
   MRCLASS = {11S40 (11M41 14E15 32S45)},
  MRNUMBER = {1151541},
MRREVIEWER = {Daniel Barsky},
       DOI = {10.2307/2152708},
       URL = {https://doi.org/10.2307/2152708},
}

@article {DM/91,
    AUTHOR = {Denef, Jan and Meuser, Diane},
     TITLE = {A functional equation of {I}gusa's local zeta function},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {113},
      YEAR = {1991},
    NUMBER = {6},
     PAGES = {1135--1152},
   MRCLASS = {11S40},
  MRNUMBER = {1137535},
MRREVIEWER = {Valeriu \c{S}t. Udrescu},
       DOI = {10.2307/2374901},
       URL = {https://doi.org/10.2307/2374901},
}

@article {Folkman:CMness,
    AUTHOR = {Folkman, Jon},
     TITLE = {The homology groups of a lattice},
   JOURNAL = {J. Math. Mech.},
    VOLUME = {15},
      YEAR = {1966},
     PAGES = {631--636},
   MRCLASS = {06.30},
  MRNUMBER = {0188116},
MRREVIEWER = {R. L. Knighten},
}

@misc{hypigu,
  author = {Maglione, Joshua},
  title = {\textsf{HypIgu}, ver.~1.0},
  note = {\texttt{\url{https://github.com/joshmaglione/hypigu}}},
  year = {2020},
}

@incollection {Igusa:Monodromy,
    AUTHOR = {Igusa, Jun-ichi},
     TITLE = {{$b$}-functions and {$p$}-adic integrals},
 BOOKTITLE = {Algebraic analysis, {V}ol. {I}},
     PAGES = {231--241},
 PUBLISHER = {Academic Press, Boston, MA},
      YEAR = {1988},
   MRCLASS = {11S80 (11M41 14G10 14G20 32C40)},
  MRNUMBER = {992457},
MRREVIEWER = {Daniel Barsky},
}

@misc{KS,
  title={A new face iterator for polyhedra and more general finite locally branched lattices}, 
  author={Jonathan Kliem and Christian Stump},
  year={2020},
  note={\texttt{\href{https://arxiv.org/abs/1905.01945}{arXiv:1905.01945}}},
}

@book {Oxley,
    AUTHOR = {Oxley, James},
     TITLE = {Matroid theory},
    SERIES = {Oxford Graduate Texts in Mathematics},
    VOLUME = {21},
   EDITION = {Second},
 PUBLISHER = {Oxford University Press, Oxford},
      YEAR = {2011},
     PAGES = {xiv+684},
   MRCLASS = {05-01 (05B35 90C27)},
  MRNUMBER = {2849819},
MRREVIEWER = {Maruti M. Shikare},
       DOI = {10.1093/acprof:oso/9780198566946.001.0001},
       URL = {https://doi.org/10.1093/acprof:oso/9780198566946.001.0001},
}

@article {Reisner:CM,
    AUTHOR = {Reisner, Gerald Allen},
     TITLE = {Cohen-{M}acaulay quotients of polynomial rings},
   JOURNAL = {Advances in Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {21},
      YEAR = {1976},
    NUMBER = {1},
     PAGES = {30--49},
   MRCLASS = {14M05 (13C10)},
  MRNUMBER = {407036},
MRREVIEWER = {Ezio Stagnaro},
       DOI = {10.1016/0001-8708(76)90114-6},
       URL = {https://doi.org/10.1016/0001-8708(76)90114-6},
}

@article {Rossmann:top-zf,
    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},
   MRCLASS = {11M41 (14E18 14G10 17A01 20F69 52B20)},
  MRNUMBER = {3349788},
MRREVIEWER = {Michael M. Schein},
       DOI = {10.1112/plms/pdv012},
}

@article{RV:CICO,
    AUTHOR = {Rossmann, Tobias and Voll, Christopher},
     TITLE = {Groups, graphs, and hypergraphs: average sizes of kernels of
              generic matrices with support constraints},
   JOURNAL = {Mem. Amer. Math. Soc.},
  FJOURNAL = {Memoirs of the American Mathematical Society},
    VOLUME = {294},
      YEAR = {2024},
    NUMBER = {1465},
     PAGES = {v+120 pp.},
      ISBN = {978-1-4704-6868-2; 978-1-4704-7753-0},
   MRCLASS = {11M41 (05A15 05C50 11S80 14M25 15B33 20D15 20E45)},
  MRNUMBER = {4719079},
       DOI = {10.1090/memo/1465},
}

@manual{sagemath,
  Key          = {SageMath},
  Author       = {{The Sage Developers}},
  Title        = {{S}ageMath, the {S}age {M}athematics {S}oftware {S}ystem ({V}ersion 9.2)},
  note         = {\texttt{\url{https://www.sagemath.org}}},
  Year         = {2020},
}

@article {ST:Poincare-poly,
    AUTHOR = {Shephard, G. C. and Todd, J. A.},
     TITLE = {Finite unitary reflection groups},
   JOURNAL = {Canad. J. Math.},
  FJOURNAL = {Canadian Journal of Mathematics. Journal Canadien de
              Math\'{e}matiques},
    VOLUME = {6},
      YEAR = {1954},
     PAGES = {274--304},
   MRCLASS = {20.0X},
  MRNUMBER = {59914},
MRREVIEWER = {H. S. M. Coxeter},
       DOI = {10.4153/cjm-1954-028-3},
       URL = {https://doi.org/10.4153/cjm-1954-028-3},
}

@article {Solomon:reflections,
    AUTHOR = {Solomon, Louis},
     TITLE = {Invariants of finite reflection groups},
   JOURNAL = {Nagoya Math. J.},
  FJOURNAL = {Nagoya Mathematical Journal},
    VOLUME = {22},
      YEAR = {1963},
     PAGES = {57--64},
   MRCLASS = {20.75 (14.08)},
  MRNUMBER = {154929},
MRREVIEWER = {R. Steinberg},
       URL = {http://projecteuclid.org/euclid.nmj/1118801157},
}

@book {Stanley:commutative,
    AUTHOR = {Stanley, Richard P.},
     TITLE = {Combinatorics and commutative algebra},
    SERIES = {Progress in Mathematics},
    VOLUME = {41},
   EDITION = {Second},
 PUBLISHER = {Birkh\"{a}user Boston, Inc., Boston, MA},
      YEAR = {1996},
     PAGES = {x+164},
   MRCLASS = {05-02 (13F50)},
  MRNUMBER = {1453579},
MRREVIEWER = {Volkmar Welker},
}

@book {Stanley:Vol1,
    AUTHOR = {Stanley, Richard P.},
     TITLE = {Enumerative combinatorics. {V}ol. 1},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {49},
   EDITION = {Second},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2012},
     PAGES = {xiv+626},
   MRCLASS = {05-02 (05A15 06-02)},
  MRNUMBER = {2868112},
}

@book {Stanley:Vol2,
    AUTHOR = {Stanley, Richard P.},
     TITLE = {Enumerative combinatorics. {V}ol. 2},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = 62,
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = 1999,
     PAGES = {xii+581},
      ISBN = {0-521-56069-1; 0-521-78987-7},
   MRCLASS = {05A15 (05-02 05E05 05E10 68R05)},
  MRNUMBER = 1676282,
MRREVIEWER = {Ira Gessel},
       DOI = {10.1017/CBO9780511609589},
       URL = {https://doi.org/10.1017/CBO9780511609589},
}

@article {Stanley:CM,
    AUTHOR = {Stanley, Richard P.},
     TITLE = {The number of faces of a simplicial convex polytope},
   JOURNAL = {Adv. in Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {35},
      YEAR = {1980},
    NUMBER = {3},
     PAGES = {236--238},
   MRCLASS = {52A25 (05B99 14M99)},
  MRNUMBER = {563925},
MRREVIEWER = {I. Dolgachev},
       DOI = {10.1016/0001-8708(80)90050-X},
       URL = {https://doi.org/10.1016/0001-8708(80)90050-X},
}

@article {Terao:generalized-exps,
    AUTHOR = {Terao, Hiroaki},
     TITLE = {Generalized exponents of a free arrangement of hyperplanes and
              {S}hepherd-{T}odd-{B}rieskorn formula},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {63},
      YEAR = {1981},
    NUMBER = {1},
     PAGES = {159--179},
   MRCLASS = {32C40 (05B25 51F15 52A45)},
  MRNUMBER = {608532},
MRREVIEWER = {P. Orlik},
       DOI = {10.1007/BF01389197},
       URL = {https://doi.org/10.1007/BF01389197},
}

@article{vanderVeer,
   title={Combinatorial analogs of topological zeta functions},
   volume={342},
   ISSN={0012-365X},
   url={http://dx.doi.org/10.1016/j.disc.2019.05.035},
   DOI={10.1016/j.disc.2019.05.035},
   number={9},
   journal={Discrete Mathematics},
   publisher={Elsevier BV},
   author={van der Veer, Robin},
   year={2019},
   month={Sep},
   pages={2680–2693}
}

@article {WW:semilattices,
    AUTHOR = {Wachs, Michelle L. and Walker, James W.},
     TITLE = {On geometric semilattices},
   JOURNAL = {Order},
  FJOURNAL = {Order},
    VOLUME = {2},
      YEAR = {1986},
    NUMBER = {4},
     PAGES = {367--385},
   MRCLASS = {06A12 (05B35 06C10)},
  MRNUMBER = {838021},
MRREVIEWER = {S. Rudeanu},
       DOI = {10.1007/BF00367425},
       URL = {https://doi.org/10.1007/BF00367425},
}

@article {Shimura/63,
    AUTHOR = {Shimura, Goro},
     TITLE = {On modular correspondences for {$Sp(n,\,Z)$} and their
              congruence relations},
   JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
  FJOURNAL = {Proceedings of the National Academy of Sciences of the United
              States of America},
    VOLUME = {49},
      YEAR = {1963},
     PAGES = {824--828},
   MRCLASS = {10.23 (32.65)},
  MRNUMBER = {157009},
MRREVIEWER = {R.\ C.\ Gunning},
       DOI = {10.1073/pnas.49.6.824},
       URL = {https://doi.org/10.1073/pnas.49.6.824},
}

@book {Fulton,
    AUTHOR = {Fulton, William},
     TITLE = {Young tableaux},
    SERIES = {London Mathematical Society Student Texts},
    VOLUME = {35},
      NOTE = {With applications to representation theory and geometry},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {1997},
     PAGES = {x+260},
      ISBN = {0-521-56144-2; 0-521-56724-6},
   MRCLASS = {05E10 (05E05 05E15 14M15 20G05)},
  MRNUMBER = {1464693},
MRREVIEWER = {Tadeusz\ J\'{o}zefiak},
}