Unimodality problems in Ehrhart theory

By Benjamin Braun. 2015

71 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/bea96d8a1d700cbd43d26d75074dea26a4a2bfbe

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In Algebra and Number Theory

1. Liam Solus
2. Petter Brand'en

In Discrete Mathematics and Combinatorics

1. Liam Solus
2. Petter Brand'en
3. Julius Borcea

Citations in the corpus

• Symmetric Decompositions and Real-Rootedness (2018, background): “The distributional properties of h(P ;x), such as unimodality and real-rootedness, are highly-investigated [11], and the following observation has recently raised new questions about the alternatingly increasing property for hpolynomials.”