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@InCollection{Ardila,
  author    = {Ardila, Federico},
  title     = {Algebraic and geometric methods in enumerative combinatorics},
  booktitle = {Handbook of enumerative combinatorics},
  publisher = {CRC Press, Boca Raton, FL},
  year      = {2015},
  series    = {Discrete Math. Appl. (Boca Raton)},
  pages     = {3--172},
  mrclass   = {05A15},
  mrnumber  = {3409342},
}

@Article{Borchardt,
  author  = {Borchardt, Carl Wilhelm},
  title   = {Ueber eine der Interpolation entsprechende Darstellung der Eliminations-Resultante.},
  journal = {Journal f{\"u}r die reine und angewandte Mathematik},
  year    = {1860},
  volume  = {57},
  pages   = {111--121},
}

@Article{Cayley,
  author  = {Cayley, Arthur},
  title   = {A theorem on trees},
  journal = {Quartery Journal of Mathematics},
  year    = {1889},
  volume  = {23},
  pages   = {376--378},
}

@Article{D'AdderioMoci,
  author     = {D'Adderio, Michele and Moci, Luca},
  title      = {{E}hrhart polynomial and arithmetic {T}utte polynomial},
  journal    = {European J. Combin.},
  year       = {2012},
  volume     = {33},
  number     = {7},
  pages      = {1479--1483},
  issn       = {0195-6698},
  doi        = {10.1016/j.ejc.2012.02.006},
  fjournal   = {European Journal of Combinatorics},
  mrclass    = {52B12 (05C31)},
  mrnumber   = {2923464},
  mrreviewer = {Ragnar Freij},
  url        = {https//0-dx.doi.org.opac.sfsu.edu/10.1016/j.ejc.2012.02.006},
}

@Book{Grunbaum,
  title      = {Convex polytopes},
  publisher  = {Springer-Verlag, New York},
  year       = {2003},
  author     = {Gr\"{u}nbaum, Branko},
  volume     = {221},
  series     = {Graduate Texts in Mathematics},
  edition    = {Second},
  isbn       = {0-387-00424-6; 0-387-40409-0},
  note       = {Prepared and with a preface by Volker Kaibel, Victor Klee and G\"{u}nter M. Ziegler},
  doi        = {10.1007/978-1-4613-0019-9},
  mrclass    = {52-01 (52Bxx)},
  mrnumber   = {1976856},
  mrreviewer = {Alexander Zvonkin},
  pages      = {xvi+468},
  url        = {https://doi-org.ezproxy.uky.edu/10.1007/978-1-4613-0019-9},
}

@Book{Sagan,
  title     = {The symmetric group},
  publisher = {Springer-Verlag, New York},
  year      = {2001},
  author    = {Sagan, Bruce E.},
  volume    = {203},
  series    = {Graduate Texts in Mathematics},
  edition   = {Second},
  isbn      = {0-387-95067-2},
  note      = {Representations, combinatorial algorithms, and symmetric functions},
  doi       = {10.1007/978-1-4757-6804-6},
  mrclass   = {05E10 (05E05 20C30)},
  mrnumber  = {1824028},
  pages     = {xvi+238},
  url       = {https://doi-org.ezproxy.uky.edu/10.1007/978-1-4757-6804-6},
}

@MastersThesis{Schindler,
  author = {Schindler, Anna},
  title  = {Algebraic and combinatorial aspects of two symmetric polytopes},
  school = {San Francisco State University},
  year   = {2017},
}

@Article{Seymour,
  author     = {Seymour, Paul D.},
  title      = {Decomposition of regular matroids},
  journal    = {J. Combin. Theory Ser. B},
  year       = {1980},
  volume     = {28},
  number     = {3},
  pages      = {305--359},
  issn       = {0095-8956},
  doi        = {10.1016/0095-8956(80)90075-1},
  fjournal   = {Journal of Combinatorial Theory. Series B},
  mrclass    = {05B35 (05C50)},
  mrnumber   = {579077},
  mrreviewer = {Thomas Brylawski},
  url        = {https://doi-org.ezproxy.uky.edu/10.1016/0095-8956(80)90075-1},
}

@InCollection{StanleyZonotope,
  author     = {Stanley, Richard P.},
  title      = {A zonotope associated with graphical degree sequences},
  booktitle  = {Applied geometry and discrete mathematics},
  publisher  = {Amer. Math. Soc., Providence, RI},
  year       = {1991},
  volume     = {4},
  series     = {DIMACS Ser. Discrete Math. Theoret. Comput. Sci.},
  pages      = {555--570},
  mrclass    = {52B20 (05C30 52B05)},
  mrnumber   = {1116376},
  mrreviewer = {P. McMullen},
}

@Book{StanleyEC1,
  title     = {Enumerative combinatorics. {V}ol. 1},
  publisher = {Cambridge University Press, Cambridge},
  year      = {2012},
  author    = {Stanley, Richard P.},
  volume    = {49},
  series    = {Cambridge Studies in Advanced Mathematics},
  edition   = {Second},
  isbn      = {978-1-107-60262-5},
  mrclass   = {05-02 (05A15 06-02)},
  mrnumber  = {2868112},
  pages     = {xiv+626},
}

@Book{StanleyEC2,
  title      = {Enumerative combinatorics. {V}ol. 2},
  publisher  = {Cambridge University Press, Cambridge},
  year       = {1999},
  author     = {Stanley, Richard P.},
  volume     = {62},
  series     = {Cambridge Studies in Advanced Mathematics},
  isbn       = {0-521-56069-1; 0-521-78987-7},
  note       = {With a foreword by Gian-Carlo Rota and appendix 1 by Sergey Fomin},
  doi        = {10.1017/CBO9780511609589},
  mrclass    = {05A15 (05-02 05E05 05E10 68R05)},
  mrnumber   = {1676282},
  mrreviewer = {Ira Gessel},
  pages      = {xii+581},
  url        = {https://doi-org.ezproxy.uky.edu/10.1017/CBO9780511609589},
}

@Article{StapledonNumbertheory,
  author     = {Stapledon, Alan},
  title      = {Additive number theory and inequalities in {E}hrhart theory},
  journal    = {Int. Math. Res. Not. IMRN},
  year       = {2016},
  number     = {5},
  pages      = {1497--1540},
  issn       = {1073-7928},
  doi        = {10.1093/imrn/rnv186},
  fjournal   = {International Mathematics Research Notices. IMRN},
  mrclass    = {52B20 (05A15 11B30 11H06)},
  mrnumber   = {3509934},
  mrreviewer = {Matthias Beck},
  url        = {https://doi-org.ezproxy.uky.edu/10.1093/imrn/rnv186},
}

@Article{StapledonEquivariant,
  author     = {Stapledon, Alan},
  title      = {Equivariant {E}hrhart theory},
  journal    = {Adv. Math.},
  year       = {2011},
  volume     = {226},
  number     = {4},
  pages      = {3622--3654},
  issn       = {0001-8708},
  doi        = {10.1016/j.aim.2010.10.019},
  fjournal   = {Advances in Mathematics},
  mrclass    = {52B20 (05A15 20C15)},
  mrnumber   = {2764900},
  mrreviewer = {Matthias Beck},
  url        = {https://doi-org.ezproxy.uky.edu/10.1016/j.aim.2010.10.019},
}

@MastersThesis{VindasMelendez,
  author = {Vindas Mel\'endez, Andr\'es R.},
  title  = {Two problems on lattice point enumeration of rational polytopes},
  school = {San Francisco State University},
  year   = {2017},
}

@Book{Sturmfels,
  title      = {Gr\"{o}bner bases and convex polytopes},
  publisher  = {American Mathematical Society, Providence, RI},
  year       = {1996},
  author     = {Sturmfels, Bernd},
  volume     = {8},
  series     = {University Lecture Series},
  isbn       = {0-8218-0487-1},
  mrclass    = {13P10 (14M25 52B20)},
  mrnumber   = {1363949},
  mrreviewer = {P. Schenzel},
  pages      = {xii+162},
}

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

@Article{ArdilaCastilloHenley,
  author     = {Ardila, Federico and Castillo, Federico and Henley, Michael},
  title      = {The arithmetic {T}utte polynomials of the classical root systems},
  journal    = {Int. Math. Res. Not. IMRN},
  year       = {2015},
  number     = {12},
  pages      = {3830--3877},
  issn       = {1073-7928},
  doi        = {10.1093/imrn/rnu050},
  fjournal   = {International Mathematics Research Notices. IMRN},
  mrclass    = {05C31 (17B22)},
  mrnumber   = {3356740},
  mrreviewer = {Seyed Amin Seyed Fakhari},
  url        = {https://doi-org.ezproxy.uky.edu/10.1093/imrn/rnu050},
}

@InCollection{BeckDeLoeraDevelinPfeifle,
  author     = {Beck, M. and De Loera, J. A. and Develin, M. and Pfeifle, J. and Stanley, R. P.},
  title      = {Coefficients and roots of {E}hrhart polynomials},
  booktitle  = {Integer points in polyhedra---geometry, number theory, algebra, optimization},
  publisher  = {Amer. Math. Soc., Providence, RI},
  year       = {2005},
  volume     = {374},
  series     = {Contemp. Math.},
  pages      = {15--36},
  doi        = {10.1090/conm/374/06897},
  mrclass    = {52B20 (05A15 52C07)},
  mrnumber   = {2134759},
  mrreviewer = {P. McMullen},
  url        = {https://doi-org.ezproxy.uky.edu/10.1090/conm/374/06897},
}

@Article{BeckJochemkoMcCullough,
  author     = {Beck, Matthias and Jochemko, Katharina and McCullough, Emily},
  title      = {{$h^\ast$}-polynomials of zonotopes},
  journal    = {Trans. Amer. Math. Soc.},
  year       = {2019},
  volume     = {371},
  number     = {3},
  pages      = {2021--2042},
  issn       = {0002-9947},
  doi        = {10.1090/tran/7384},
  fjournal   = {Transactions of the American Mathematical Society},
  mrclass    = {52B20 (05A15 05B35 52B40 52B45)},
  mrnumber   = {3894043},
  mrreviewer = {Matthias Schymura},
  url        = {https://doi-org.ezproxy.uky.edu/10.1090/tran/7384},
}

@Book{BeckRobins,
  title     = {Computing the continuous discretely},
  publisher = {Springer, New York},
  year      = {2015},
  author    = {Beck, Matthias and Robins, Sinai},
  series    = {Undergraduate Texts in Mathematics},
  edition   = {Second},
  isbn      = {978-1-4939-2968-9; 978-1-4939-2969-6},
  note      = {Integer-point enumeration in polyhedra, With illustrations by David Austin},
  doi       = {10.1007/978-1-4939-2969-6},
  mrclass   = {11P21 (05A15 05B15 11-02 11H06 52B05 52B20)},
  mrnumber  = {3410115},
  pages     = {xx+285},
  url       = {https://doi-org.ezproxy.uky.edu/10.1007/978-1-4939-2969-6},
}

@InCollection{Braun,
  author     = {Braun, Benjamin},
  title      = {Unimodality problems in {E}hrhart theory},
  booktitle  = {Recent trends in combinatorics},
  publisher  = {Springer, [Cham]},
  year       = {2016},
  volume     = {159},
  series     = {IMA Vol. Math. Appl.},
  pages      = {687--711},
  doi        = {10.1007/978-3-319-24298-9_27},
  mrclass    = {52B20 (05A20)},
  mrnumber   = {3526428},
  mrreviewer = {Ruriko Yoshida},
  url        = {https://doi-org.ezproxy.uky.edu/10.1007/978-3-319-24298-9_27},
}

@Misc{DallPfeifle,
  author = {Dall, Aaron, and Pfeifle, Julian},
  title  = {A Polyhedral Proof of the Matrix Tree Theorem},
  note   = {preprint (arXiv:1404.3876)},
}

@Article{Ehrhart,
  author   = {Ehrhart, Eug\`ene},
  title    = {Sur les poly\`edres rationnels homoth\'{e}tiques \`a {$n$}\ dimensions},
  journal  = {C. R. Acad. Sci. Paris},
  year     = {1962},
  volume   = {254},
  pages    = {616--618},
  mrclass  = {10.25 (52.10)},
  mrnumber = {0130860},
}

@Article{Grujic,
  author     = {Gruji\'{c}, Vladimir},
  title      = {Counting faces of graphical zonotopes},
  journal    = {Ars Math. Contemp.},
  year       = {2017},
  volume     = {13},
  number     = {1},
  pages      = {227--234},
  issn       = {1855-3966},
  doi        = {10.26493/1855-3974.1132.fae},
  fjournal   = {Ars Mathematica Contemporanea},
  mrclass    = {05E05 (16T05 52B05)},
  mrnumber   = {3669576},
  mrreviewer = {Evgeny Smirnov},
  url        = {https://doi-org.ezproxy.uky.edu/10.26493/1855-3974.1132.fae},
}

@Misc{HopkinsPostnikov,
  author = {Hopkins, Sam and Postnikov, Alexander},
  title  = {A positive formula for the {E}hrhart-like polynomials from root system chip-firing},
  note   = {preprint (arXiv:1803.08472)},
}

@Article{Moci,
  author     = {Moci, Luca},
  title      = {A {T}utte polynomial for toric arrangements},
  journal    = {Trans. Amer. Math. Soc.},
  year       = {2012},
  volume     = {364},
  number     = {2},
  pages      = {1067--1088},
  issn       = {0002-9947},
  doi        = {10.1090/S0002-9947-2011-05491-7},
  fjournal   = {Transactions of the American Mathematical Society},
  mrclass    = {05B35 (05C31 17B22 52B40 52C35)},
  mrnumber   = {2846363},
  mrreviewer = {Tom C. Braden},
  url        = {https://doi-org.ezproxy.uky.edu/10.1090/S0002-9947-2011-05491-7},
}

@Article{Postnikov,
  author   = {Postnikov, Alexander},
  title    = {Permutohedra, associahedra, and beyond},
  journal  = {Int. Math. Res. Not. IMRN},
  year     = {2009},
  number   = {6},
  pages    = {1026--1106},
  issn     = {1073-7928},
  doi      = {10.1093/imrn/rnn153},
  fjournal = {International Mathematics Research Notices. IMRN},
  mrclass  = {05E30},
  mrnumber = {2487491},
  url      = {https://doi-org.ezproxy.uky.edu/10.1093/imrn/rnn153},
}

@Article{Shephard,
  author     = {Shephard, Geoffrey C.},
  title      = {Combinatorial properties of associated zonotopes},
  journal    = {Canad. J. Math.},
  year       = {1974},
  volume     = {26},
  pages      = {302--321},
  issn       = {0008-414X},
  doi        = {10.4153/CJM-1974-032-5},
  fjournal   = {Canadian Journal of Mathematics. Journal Canadien de Math\'{e}matiques},
  mrclass    = {52A25},
  mrnumber   = {0362054},
  mrreviewer = {Joseph Zaks},
  url        = {https://doi-org.ezproxy.uky.edu/10.4153/CJM-1974-032-5},
}

@Article{StanleyDecompositions,
  author     = {Stanley, Richard P.},
  title      = {Decompositions of rational convex polytopes},
  journal    = {Ann. Discrete Math.},
  year       = {1980},
  volume     = {6},
  pages      = {333--342},
  note       = {Combinatorial mathematics, optimal designs and their applications (Proc. Sympos. Combin. Math. and Optimal Design, Colorado State Univ., Fort Collins, Colo., 1978)},
  fjournal   = {Annals of Discrete Mathematics},
  mrclass    = {52A43},
  mrnumber   = {593545},
  mrreviewer = {P. McMullen},
}

@InCollection{StanleyUnimodality,
  author     = {Stanley, Richard P.},
  title      = {Log-concave and unimodal sequences in algebra, combinatorics, and geometry},
  booktitle  = {Graph theory and its applications: {E}ast and {W}est ({J}inan, 1986)},
  publisher  = {New York Acad. Sci., New York},
  year       = {1989},
  volume     = {576},
  series     = {Ann. New York Acad. Sci.},
  pages      = {500--535},
  doi        = {10.1111/j.1749-6632.1989.tb16434.x},
  mrclass    = {05E15 (05E10 20C15 52B20)},
  mrnumber   = {1110850},
  mrreviewer = {L. Bruce Richmond},
  url        = {https://doi-org.ezproxy.uky.edu/10.1111/j.1749-6632.1989.tb16434.x},
}

@Article{StapledonInequalities,
  author     = {Stapledon, Alan},
  title      = {Inequalities and {E}hrhart {$\delta$}-vectors},
  journal    = {Trans. Amer. Math. Soc.},
  year       = {2009},
  volume     = {361},
  number     = {10},
  pages      = {5615--5626},
  issn       = {0002-9947},
  doi        = {10.1090/S0002-9947-09-04776-X},
  fjournal   = {Transactions of the American Mathematical Society},
  mrclass    = {52B20},
  mrnumber   = {2515826},
  mrreviewer = {Benjamin Braun},
}

@Article{Zong,
  author     = {Zong, Chuanming},
  title      = {What is known about unit cubes},
  journal    = {Bull. Amer. Math. Soc. (N.S.)},
  year       = {2005},
  volume     = {42},
  number     = {2},
  pages      = {181--211},
  issn       = {0273-0979},
  doi        = {10.1090/S0273-0979-05-01050-5},
  fjournal   = {American Mathematical Society. Bulletin. New Series},
  mrclass    = {52C20 (05A15 05B25 05B45 11H31 52B05 52C22)},
  mrnumber   = {2133310},
  mrreviewer = {Martin Henk},
  url        = {https://doi-org.ezproxy.uky.edu/10.1090/S0273-0979-05-01050-5},
}

@InCollection{BraunVindasMelendez,
  author    = {Braun, Benjamin and Vindas-Mel\'{e}ndez, Andr\'{e}s R.},
  title     = {A brief survey on lattice zonotopes},
  booktitle = {Algebraic and geometric combinatorics on lattice polytopes},
  publisher = {World Sci. Publ., Hackensack, NJ},
  year      = {2019},
  pages     = {101--116},
  mrclass   = {52B20 (05E05)},
  mrnumber  = {3971688},
}

@Misc{AguiarArdila,
  author = {Aguiar, Marcelo and Ardila, Federico},
  title  = {The Hopf monoid of generalized permutahedra},
  note   = {unpublished manuscript},
}

@Article{HibiHilbertFunctions,
  author     = {Hibi, Takayuki},
  title      = {Hilbert functions of {C}ohen-{M}acaulay integral domains and chain conditions of finite partially ordered sets},
  journal    = {J. Pure Appl. Algebra},
  year       = {1991},
  volume     = {72},
  number     = {3},
  pages      = {265--273},
  issn       = {0022-4049},
  doi        = {10.1016/0022-4049(91)90065-A},
  fjournal   = {Journal of Pure and Applied Algebra},
  mrclass    = {13D40 (06A07 13H10)},
  mrnumber   = {1120693},
  mrreviewer = {Matthew Miller},
  url        = {https://doi-org.ezproxy.uky.edu/10.1016/0022-4049(91)90065-A},
}

@Article{StanleyHilbertFunctions,
  author     = {Stanley, Richard P.},
  title      = {Hilbert functions of graded algebras},
  journal    = {Advances in Math.},
  year       = {1978},
  volume     = {28},
  number     = {1},
  pages      = {57--83},
  issn       = {0001-8708},
  doi        = {10.1016/0001-8708(78)90045-2},
  fjournal   = {Advances in Mathematics},
  mrclass    = {13D10 (13H10)},
  mrnumber   = {0485835},
  mrreviewer = {Idun Reiten},
  url        = {https://doi-org.ezproxy.uky.edu/10.1016/0001-8708(78)90045-2},
}

@Article{StanleyHilbertFunctionCohenMacaulay,
  author     = {Stanley, Richard P.},
  title      = {On the {H}ilbert function of a graded {C}ohen-{M}acaulay domain},
  journal    = {J. Pure Appl. Algebra},
  year       = {1991},
  volume     = {73},
  number     = {3},
  pages      = {307--314},
  issn       = {0022-4049},
  doi        = {10.1016/0022-4049(91)90034-Y},
  fjournal   = {Journal of Pure and Applied Algebra},
  mrclass    = {13D40 (13A02 13H10 52B20)},
  mrnumber   = {1124790},
  mrreviewer = {Matthew Miller},
}

@Article{HibiEhrhartPolynomials,
  author     = {Hibi, Takayuki},
  title      = {Some results on {E}hrhart polynomials of convex polytopes},
  journal    = {Discrete Math.},
  year       = {1990},
  volume     = {83},
  number     = {1},
  pages      = {119--121},
  issn       = {0012-365X},
  doi        = {10.1016/0012-365X(90)90226-8},
  fjournal   = {Discrete Mathematics},
  mrclass    = {52B20 (06A08)},
  mrnumber   = {1065691},
  mrreviewer = {Bernd Graw},
}

@Article{Hochster,
  author     = {Hochster, M.},
  title      = {Rings of invariants of tori, {C}ohen-{M}acaulay rings generated by monomials, and polytopes},
  journal    = {Ann. of Math. (2)},
  year       = {1972},
  volume     = {96},
  pages      = {318--337},
  issn       = {0003-486X},
  doi        = {10.2307/1970791},
  fjournal   = {Annals of Mathematics. Second Series},
  mrclass    = {13H10 (20G05)},
  mrnumber   = {0304376},
  mrreviewer = {Tadayuki Matsuoka},
  url        = {https://doi-org.ezproxy.uky.edu/10.2307/1970791},
}

@Book{HibiAlgCom,
  title     = {Algebraic combinatorics on convex polytopes},
  publisher = {Carslaw Publications, Glebe},
  year      = {1992},
  author    = {Hibi, Takayuki},
  isbn      = {1-875399-04-6},
  mrclass   = {52-02 (05E45 13F55 57Q05)},
  mrnumber  = {3183743},
  pages     = {x+164},
}

@Book{BrunsGubeladze,
  title      = {Polytopes, rings, and {$K$}-theory},
  publisher  = {Springer, Dordrecht},
  year       = {2009},
  author     = {Bruns, Winfried and Gubeladze, Joseph},
  series     = {Springer Monographs in Mathematics},
  isbn       = {978-0-387-76355-2},
  doi        = {10.1007/b105283},
  mrclass    = {19-02 (11H06 13F45 14M25 52-01 52B20)},
  mrnumber   = {2508056},
  mrreviewer = {T. Oda},
  pages      = {xiv+461},
  url        = {https://doi-org.ezproxy.uky.edu/10.1007/b105283},
}

@Misc{M2,
  author       = {Grayson, Daniel R. and Stillman, Michael E.},
  title        = {Macaulay2, a software system for research in algebraic geometry},
  howpublished = {Available at \url{http://www.math.uiuc.edu/Macaulay2/}},
}

@Article{ASV,
  author       = {{Ardila}, Federico and {Schindler}, Anna and {Vindas-Mel{\'e}ndez}, Andr{\'e}s R.},
  title        = {{The equivariant volumes of the permutahedron}},
  journal      = {Discrete and Computational Geometry},
  year         = {2019},
  pages        = {1-18},
  keywords     = {Mathematics - Combinatorics, 05E18, 52A38, 52B15},
  primaryclass = {math.CO},
}

@Book{Coxeter,
  title     = {Regular polytopes},
  publisher = {Methuen},
  year      = {1948},
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@Article{StanleyMonotonicity,
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@Article{DezaManoussakisOnn1,
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@InCollection{DezaManoussakisOnn2,
  author     = {Deza, Antoine and Manoussakis, George and Onn, Shmuel},
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  series     = {Springer Proc. Math. Stat.},
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@Misc{Hopkins,
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@MastersThesis{McWhirter,
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@Misc{ASV2,
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@Book{MillerSturmfels,
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@Article{Pommersheim,
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@Article{StapledonRepresentations,
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@Book{Fulton,
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@Article{FisetKasprzyk,
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@Article{Athanasiadis,
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@Article{Macdonald,
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@Article{KasprzykNill,
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@Misc{StapledonGeometric,
  author        = {Alan Stapledon},
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  year          = {2008},
  note          = {preprint (arXiv:0807.3543)},
  archiveprefix = {arXiv},
  eprint        = {0807.3543},
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@Article{JochemkoSanyal,
  author     = {Jochemko, Katharina and Sanyal, Raman},
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@Article{BeckSottile,
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@Article{HibiDual,
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@Article{BaldoniVergne,
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@Book{CoxLittleSchenck,
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@Article{StapledonMirror,
  author    = {Stapledon, Alan},
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@Misc{BeckBraunVindas,
  author        = {Matthias Beck and Benjamin Braun and Andr\'es R. Vindas-Mel\'endez},
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  eprint        = {2006.10076},
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@InCollection{Ziegler0/1,
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  series    = {DMV Sem.},
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@Article{GelfandKapranovZelevinksy,
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@Article{Batyrev,
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  mrnumber   = {1269718},
  mrreviewer = {I. Dolgachev},
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@Article{BraunReflexive,
  author     = {Braun, Benjamin},
  title      = {An {E}hrhart series formula for reflexive polytopes},
  journal    = {Electron. J. Combin.},
  year       = {2006},
  volume     = {13},
  number     = {1},
  pages      = {Note 15, 5},
  fjournal   = {Electronic Journal of Combinatorics},
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  mrnumber   = {2255415},
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  url        = {http://www.combinatorics.org/Volume_13/Abstracts/v13i1n15.html},
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@Article{HibiTsuchiyaReflexiveGraphs,
  author     = {Hibi, Takayuki and Tsuchiya, Akiyoshi},
  title      = {Reflexive polytopes arising from perfect graphs},
  journal    = {J. Combin. Theory Ser. A},
  year       = {2018},
  volume     = {157},
  pages      = {233--246},
  issn       = {0097-3165},
  doi        = {10.1016/j.jcta.2018.02.012},
  fjournal   = {Journal of Combinatorial Theory. Series A},
  mrclass    = {52B20 (05C17)},
  mrnumber   = {3780413},
  mrreviewer = {Margaret M. Bayer},
  url        = {https://doi-org.ezproxy.uky.edu/10.1016/j.jcta.2018.02.012},
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@Article{HeSeongYau,
  author     = {He, Yang-Hui and Seong, Rak-Kyeong and Yau, Shing-Tung},
  title      = {Calabi-{Y}au volumes and reflexive polytopes},
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  year       = {2018},
  volume     = {361},
  number     = {1},
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  fjournal   = {Communications in Mathematical Physics},
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  mrnumber   = {3825939},
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@Article{BraunDavisSolus,
  author     = {Braun, Benjamin and Davis, Robert and Solus, Liam},
  title      = {Detecting the integer decomposition property and {E}hrhart unimodality in reflexive simplices},
  journal    = {Adv. in Appl. Math.},
  year       = {2018},
  volume     = {100},
  pages      = {122--142},
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  fjournal   = {Advances in Applied Mathematics},
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  mrnumber   = {3835192},
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  url        = {https://doi-org.ezproxy.uky.edu/10.1016/j.aam.2018.06.003},
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@Article{NagaokaTsuchiya,
  author     = {Nagaoka, Takahiro and Tsuchiya, Akiyoshi},
  title      = {Reflexive polytopes arising from edge polytopes},
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  year       = {2018},
  volume     = {557},
  pages      = {438--454},
  issn       = {0024-3795},
  doi        = {10.1016/j.laa.2018.08.012},
  fjournal   = {Linear Algebra and its Applications},
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  mrnumber   = {3848281},
  mrreviewer = {Ruriko Yoshida},
  url        = {https://doi-org.ezproxy.uky.edu/10.1016/j.laa.2018.08.012},
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@Article{HibiTsuchiyaReflexive,
  author     = {Hibi, Takayuki and Tsuchiya, Akiyoshi},
  title      = {Reflexive polytopes arising from partially ordered sets and perfect graphs},
  journal    = {J. Algebraic Combin.},
  year       = {2019},
  volume     = {49},
  number     = {1},
  pages      = {69--81},
  issn       = {0925-9899},
  doi        = {10.1007/s10801-018-0817-3},
  fjournal   = {Journal of Algebraic Combinatorics. An International Journal},
  mrclass    = {52B20 (13P10)},
  mrnumber   = {3908356},
  mrreviewer = {G\'{a}bor Hetyei},
  url        = {https://doi-org.ezproxy.uky.edu/10.1007/s10801-018-0817-3},
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@Article{HegedusHigashitaniKasprzyk,
  author     = {Heged\"{u}s, G\'{a}bor and Higashitani, Akihiro and Kasprzyk, Alexander},
  title      = {Ehrhart polynomial roots of reflexive polytopes},
  journal    = {Electron. J. Combin.},
  year       = {2019},
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  number     = {1},
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  doi        = {10.37236/7780},
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  mrnumber   = {3934369},
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  url        = {https://doi-org.ezproxy.uky.edu/10.37236/7780},
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@Article{HibiTsuchiyaDepth,
  author   = {Hibi, Takayuki and Tsuchiya, Akiyoshi},
  title    = {The depth of a reflexive polytope},
  journal  = {Arch. Math. (Basel)},
  year     = {2019},
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  number   = {3},
  pages    = {265--272},
  issn     = {0003-889X},
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@Misc{Normaliz,
  author       = {Bruns, Winfried and Ichim, Bogdan and R\"omer, Tim and Sieg, Richard and S\"oger, Christof},
  title        = {Normaliz. Algorithms for rational cones and affine monoids},
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@Article{Leon,
  author     = {Le\'{o}n, Emerson},
  title      = {Stapledon decompositions and inequalities for coefficients of chromatic polynomials},
  journal    = {S\'{e}m. Lothar. Combin.},
  year       = {2017},
  volume     = {78B},
  pages      = {Art. 24, 12},
  doi        = {10.1155/2017/1084769},
  fjournal   = {S\'{e}minaire Lotharingien de Combinatoire},
  mrclass    = {52B20 (05E05)},
  mrnumber   = {3678606},
  mrreviewer = {Ruriko Yoshida},
  url        = {https://doi-org.ezproxy.uky.edu/10.1155/2017/1084769},
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@Misc{JochemkoSymmetric,
  author        = {Katharina Jochemko},
  title         = {Symmetric Decompositions and the {V}eronese Construction},
  year          = {2020},
  note          = {preprint (arXiv:2004.05423)},
  archiveprefix = {arXiv},
  eprint        = {2004.05423},
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@Article{JochemkoReal-Rootedness,
  author     = {Jochemko, Katharina},
  title      = {On the real-rootedness of the {V}eronese construction for rational formal power series},
  journal    = {Int. Math. Res. Not. IMRN},
  year       = {2018},
  number     = {15},
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  issn       = {1073-7928},
  doi        = {10.1093/imrn/rnx027},
  fjournal   = {International Mathematics Research Notices. IMRN},
  mrclass    = {13D40 (52B20)},
  mrnumber   = {3842377},
  mrreviewer = {Seth Sullivant},
  url        = {https://doi-org.ezproxy.uky.edu/10.1093/imrn/rnx027},
}

@Book{StanleyGreenBook,
  title      = {Combinatorics and commutative algebra},
  publisher  = {Birkh\"{a}user Boston, Inc., Boston, MA},
  year       = {1996},
  author     = {Stanley, Richard P.},
  volume     = {41},
  series     = {Progress in Mathematics},
  edition    = {Second},
  isbn       = {0-8176-3836-9},
  mrclass    = {05-02 (13F50)},
  mrnumber   = {1453579},
  mrreviewer = {Volkmar Welker},
  pages      = {x+164},
}

@Misc{BrandenSolus,
  author        = {Petter Brändén and Liam Solus},
  title         = {Symmetric decompositions and real-rootedness},
  year          = {2018},
  note          = {To appear in the International Mathematics Research Notices},
  archiveprefix = {arXiv},
  eprint        = {1808.04141},
  primaryclass  = {math.CO},
}

@Article{StanleySubdivisions,
  author     = {Stanley, Richard P.},
  title      = {Subdivisions and local {$h$}-vectors},
  journal    = {J. Amer. Math. Soc.},
  year       = {1992},
  volume     = {5},
  number     = {4},
  pages      = {805--851},
  issn       = {0894-0347},
  doi        = {10.2307/2152711},
  fjournal   = {Journal of the American Mathematical Society},
  mrclass    = {52B20 (05E99 06A07 13D40 55U10)},
  mrnumber   = {1157293},
  mrreviewer = {Margaret M. Bayer},
  url        = {https://doi-org.ezproxy.uky.edu/10.2307/2152711},
}

@Book{McMullenShephard,
  title      = {Convex polytopes and the upper bound conjecture},
  publisher  = {Cambridge University Press, London-New York},
  year       = {1971},
  author     = {McMullen, Peter and Shephard, Geoffrey C.},
  note       = {Prepared in collaboration with J. E. Reeve and A. A. Ball, London Mathematical Society Lecture Note Series, 3},
  mrclass    = {52A25},
  mrnumber   = {0301635},
  mrreviewer = {H. S. M. Coxeter},
  pages      = {iv+184},
}

@Article{StanleyFaces,
  author     = {Stanley, Richard P.},
  title      = {The number of faces of a simplicial convex polytope},
  journal    = {Adv. in Math.},
  year       = {1980},
  volume     = {35},
  number     = {3},
  pages      = {236--238},
  issn       = {0001-8708},
  doi        = {10.1016/0001-8708(80)90050-X},
  fjournal   = {Advances in Mathematics},
  mrclass    = {52A25 (05B99 14M99)},
  mrnumber   = {563925},
  mrreviewer = {I. Dolgachev},
  url        = {https://doi-org.ezproxy.uky.edu/10.1016/0001-8708(80)90050-X},
}

@Comment{jabref-meta: databaseType:bibtex;}