English

Unimodality Problems in Ehrhart Theory

Combinatorics 2017-11-30 v3

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 hh^*-vector. Ehrhart hh^*-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 hh^*-vectors and highlight open questions and problems.

Keywords

Cite

@article{arxiv.1505.07377,
  title  = {Unimodality Problems in Ehrhart Theory},
  author = {Benjamin Braun},
  journal= {arXiv preprint arXiv:1505.07377},
  year   = {2017}
}

Comments

Published in Recent Trends in Combinatorics, Beveridge, A., et al. (eds), Springer, 2016, pp 687-711, doi 10.1007/978-3-319-24298-9_27. This version updated October 2017 to correct an error in the original version

R2 v1 2026-06-22T09:42:30.416Z