Lower bounds on the coefficients of Ehrhart polynomials

被引：19

作者：

Henk, Martin ^{[1
]}

Tagami, Makoto ^{[1
]}

机构：

[1] Univ Magdeburg, Inst Algebra & Geometrie, D-39106 Magdeburg, Germany

来源：

EUROPEAN JOURNAL OF COMBINATORICS | 2009年 / 30卷 / 01期

基金：

日本学术振兴会;

关键词：

GEOMETRIE DIOPHANTIENNE; ROOTS;

D O I：

10.1016/j.ejc.2008.02.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present lower bounds for the coefficients of Ehrhart polynomials of convex lattice polytopes in terms of their volume. Concerning the coefficients of the Ehrhart series of a lattice polytope we show that Hibi's lower bound is not true for lattice polytopes without interior lattice points. The counterexample is based on a formula of the Ehrhart series of the join of two lattice polytope. We also present a formula for calculating the Ehrhart series of integral dilates of a polytope. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：70 / 83

页数：14

共 50 条

[41] Ehrhart polynomials and successive minima
Henk, Martin
Schuermann, Achill
Wills, Joerg M.
MATHEMATIKA, 2005, 52 (103-04) : 1 - 16
[42] Ehrhart polynomials of cyclic polytopes
Liu, F
JOURNAL OF COMBINATORIAL THEORY SERIES A, 2005, 111 (01) : 111 - 127
[43] Notes on the Roots of Ehrhart Polynomials
Christian Bey
Martin Henk
Jorg M. Wills
Discrete & Computational Geometry, 2007, 38 : 81 - 98
[44] LOWER BOUNDS FOR NORMAL STRUCTURE COEFFICIENTS
BENAVIDES, TD
ACEDO, GL
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1992, 121 : 245 - 252
[45] On Ehrhart Polynomials of Lattice Triangles
Hofscheier, Johannes
Nill, Benjamin
Oberg, Dennis
ELECTRONIC JOURNAL OF COMBINATORICS, 2018, 25 (01):
[46] Lower bounds for decomposable univariate wild polynomials
von zur Gathen, Joachim
JOURNAL OF SYMBOLIC COMPUTATION, 2013, 50 : 409 - 430
[47] Nonclassical Polynomials as a Barrier to Polynomial Lower Bounds
Bhowmick, Abhishek
Lovett, Shachar
30TH CONFERENCE ON COMPUTATIONAL COMPLEXITY (CCC 2015), 2015, 33 : 72 - 87
[48] Some lower bounds for the derivative of certain polynomials
Dar I.
Iqbal A.
ANNALI DELL'UNIVERSITA' DI FERRARA, 2020, 66 (2) : 295 - 300
[49] LOWER BOUNDS FOR POLYNOMIALS USING GEOMETRIC PROGRAMMING
Ghasemi, Mehdi
Marshall, Murray
SIAM JOURNAL ON OPTIMIZATION, 2012, 22 (02) : 460 - 473
[50] Bounds on Autocorrelation Coefficients of Rudin-Shapiro Polynomials
Allouche, J. -P.
Choi, S.
Denise, A.
Erdelyi, T.
Saffari, B.
ANALYSIS MATHEMATICA, 2019, 45 (04) : 705 - 726

← 1 2 3 4 5 →