Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 60: Issue 2-3
Refined Ehrhart Series and Bigraded Rings
Authors:
Praise Adeyemo Faculty of Science, University of Ibadan, Ibadan, Oyo State, Nigeria

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and
Balázs Szendrői Department of Mathematics, University of Vienna, Vienna, Austria

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Pages:
97–108
Online Publication Date:
24 Oct 2023
Publication Date:
24 Oct 2023
Article Category:
Research Article
DOI:
https://doi.org/10.1556/012.2023.01541
Keywords:
Ehrhart series; 𝒒-refinement; toric variety
Restricted access

We study a natural set of refinements of the Ehrhart series of a closed polytope, first considered by Chapoton. We compute the refined series in full generality for a simplex of dimension 𝑑, a cross-polytope of dimension 𝑑, respectively a hypercube of dimension 𝑑 ≤ 3, using commutative algebra. We deduce summation formulae for products of 𝑞-integers with different arguments, generalizing a classical identity due to MacMahon and Carlitz. We also present a characterisation of a certain refined Eulerian polynomial in algebraic terms.

  • [1]

    P. Adeyemo. Grassmannians in the lattice points of dilations of standard simplex. arXiv:2207.03683.

  • [2]

    M. Beck and S. Robins. Computing the Continuous Discretely. Integer-Point Enumeration in Polyhedra, UTM 154. Springer, New York, 2007.

  • [3]

    M. Beck and R. Sanyal. Combinatorial Reciprocity Theorems. An Invitation To Enumerative Geometric Combinatorics, GSM 195. AMS, Providence, R. I., 2018.

    • Search Google Scholar
    • Export Citation
  • [4]

    L. Carlitz. A combinatorial property of 𝑞-Eulerian numbers. Amer. Math. Monthly, 82:51–54, 1975.

  • [5]

    F. Chapoton. 𝑞-analogues of Ehrhart polynomials. Proc. Edinb. Math. Soc. (2) 59:339–358, 2016.

  • [6]

    C.-O. Chow and I. M. Gessel. On the descent numbers and major indices for the hyperoctahedral group. Advances in Applied Mathematics 38:275–301, 2007.

    • Search Google Scholar
    • Export Citation
  • [7]

    P. A. MacMahon. Two applications of general theorems in combinatory analysis: (1) to the theory of inversion of permutations; (2) to the ascertainment of the numbers of terms in the development of a determinant which has amongst its elements an arbitrary number of zeros. Proc. London Math. Soc. (2) 15:314–321, 1916.

    • Search Google Scholar
    • Export Citation
  • [8]

    M. Michalek and B. Sturmfels. Invitation to non-linear algebra. Graduate Studies in Mathematics 172. AMS, Providence, R. I., 2021.

  • [9]

    R. P. Stanley. Ordered structures and partitions. Memoirs of the AMS 119. Providence, R. I., 1972.

  • [10]

    R. P. Stanley. Magic labelings of graphs, symmetric magic squares, systems of parameters, and Cohen-Macaulay rings. Duke M. J. 43:511–531, 1976.

    • Search Google Scholar
    • Export Citation
  • [11]

    B. Sturmfels. Gröbner bases and convex polytopes. University Lecture Series 8. AMS, Providence, R. I., 1996.

  • [12]

    E. Tielker. Weighted Ehrhart series and a type-B analogue of a formula of MacMahon. arXiv:2203.15774.

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Cover Studia Scientiarum Mathematicarum Hungarica
Studia Scientiarum Mathematicarum Hungarica
Print ISSN:
0081-6906
Online ISSN:
1588-2896

Editors in Chief

Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics) 

Managing Editor

Gábor SÁGI (Rényi Institute of Mathematics)

Editorial Board

  • Imre BÁRÁNY (Rényi Institute of Mathematics)
  • Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
  • Péter CSIKVÁRI (ELTE, Budapest) 
  • Joshua GREENE (Boston College)
  • Penny HAXELL (University of Waterloo)
  • Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
  • Ron HOLZMAN (Technion, Haifa)
  • Satoru IWATA (University of Tokyo)
  • Tibor JORDÁN (ELTE, Budapest)
  • Roy MESHULAM (Technion, Haifa)
  • Frédéric MEUNIER (École des Ponts ParisTech)
  • Márton NASZÓDI (ELTE, Budapest)
  • Eran NEVO (Hebrew University of Jerusalem)
  • János PACH (Rényi Institute of Mathematics)
  • Péter Pál PACH (BME, Budapest)
  • Andrew SUK (University of California, San Diego)
  • Zoltán SZABÓ (Princeton University)
  • Martin TANCER (Charles University, Prague)
  • Gábor TARDOS (Rényi Institute of Mathematics)
  • Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
Language English
French
German
Size B5
Year of
Foundation		 1966
Volumes
per Year		 1
Issues
per Year		 4
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)

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