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math.CO2023
Examples and counterexamples in Ehrhart theory
Luis Ferroni, Akihiro Higashitani
This article provides a comprehensive exposition about inequalities that the coefficients of Ehrhart polynomials and -polynomials satisfy under various assumptions. We pay par…
math.CO2023
Ehrhart quasi-polynomials and parallel translations
Akihiro Higashitani, Satoshi Murai, Masahiko Yoshinaga
Given a rational polytope , the numerical function counting lattice points in the integral dilations of is known to become a quasi-polynomial, called the…
math.CO2023
Adjacency matrices over a finite prime field and their direct sum decompositions
Akihiro Higashitani, Yuya Sugishita
In this paper, we discuss the adjacency matrices of finite undirected simple graphs over a finite prime field . We apply symmetric (row and column) elementary transfo…