Unimodality Problems in Ehrhart Theory

2015/05/27 by Benjamin Braun, Braun, Benjamin · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1505.07377

openalex publication_date 2015/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Ehrhart theory is the study of sequences recording the number of integer points in non-negative integral dilates of rational polytopes. For a given lattice polytope, this sequence is encoded in a finite vector called the Ehrhart h^*-vector. Ehrhart h^*-vectors have connections to many areas of mathematics, including commutative algebra and enumerative combinatorics. In this survey we discuss what is known about unimodality for Ehrhart h^*-vectors and highlight open questions and problems.

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• Weighted Ehrhart functions

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