Ehrhart polynomials of polytopes and spectrum at infinity of Laurent polynomials

被引：2
|
作者：
Douai, Antoine [1 ]
机构：
[1] Univ Cote Azur, CNRS, LJAD, Nice, France
来源：
JOURNAL OF ALGEBRAIC COMBINATORICS | 2021年 / 54卷 / 03期
关键词：
Toric varieties; Polytopes; Ehrhart theory; Spectrum of polytopes; Spectrum of regular functions;
D O I：
10.1007/s10801-020-00984-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Gathering different results from singularity theory, geometry and combinatorics, we show that the spectrum at infinity of a tame Laurent polynomial counts (weighted) lattice points in polytopes. We deduce an effective algorithm in order to compute the Ehrhart polynomial of a simplex containing the origin as an interior point.
引用
收藏
页码：719 / 732
页数：14
相关论文
共 50 条
  • [31] Characteristic and Ehrhart polynomials
    Blass, A
    Sagan, BE
    [J]. JOURNAL OF ALGEBRAIC COMBINATORICS, 1998, 7 (02) : 115 - 126
  • [32] Ehrhart tensor polynomials
    Berg, Soeren
    Jochemko, Katharina
    Silverstein, Laura
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2018, 539 : 72 - 93
  • [33] GENERALIZED EHRHART POLYNOMIALS
    Chen, Sheng
    Li, Nan
    Sam, Steven V.
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 364 (01) : 551 - 569
  • [34] Flat -vectors and their Ehrhart polynomials
    Hibi, Takayuki
    Tsuchiya, Akiyoshi
    [J]. ARCHIV DER MATHEMATIK, 2017, 108 (02) : 151 - 157
  • [35] Ehrhart polynomials and successive minima
    Henk, Martin
    Schuermann, Achill
    Wills, Joerg M.
    [J]. MATHEMATIKA, 2005, 52 (103-04) : 1 - 16
  • [36] Notes on the roots of Ehrhart polynomials
    Bey, Christian
    Henk, Martin
    Wills, Joerg M.
    [J]. DISCRETE & COMPUTATIONAL GEOMETRY, 2007, 38 (01) : 81 - 98
  • [37] Coefficients and roots of Ehrhart polynomials
    Beck, M
    De Loera, JA
    Develin, M
    Pfeifle, J
    Stanley, RP
    [J]. INTEGER POINTS IN POLYHEDRA-GEOMETRY, NUMBER THEORY, ALGEBRA, OPTIMIZATION, 2005, 374 : 15 - 36
  • [38] Notes on the Roots of Ehrhart Polynomials
    Christian Bey
    Martin Henk
    Jorg M. Wills
    [J]. Discrete & Computational Geometry, 2007, 38 : 81 - 98
  • [39] On Ehrhart Polynomials of Lattice Triangles
    Hofscheier, Johannes
    Nill, Benjamin
    Oberg, Dennis
    [J]. ELECTRONIC JOURNAL OF COMBINATORICS, 2018, 25 (01):
  • [40] Ehrhart Polynomials with Negative Coefficients
    Hibi, Takayuki
    Higashitani, Akihiro
    Tsuchiya, Akiyoshi
    Yoshida, Koutarou
    [J]. GRAPHS AND COMBINATORICS, 2019, 35 (01) : 363 - 371
12345