An Extension of hibi's palindromic theorem

TL;DR

This paper extends Hibi's palindromic theorem to graph polytopes of bipartite graphs, proving the numerator polynomial of their Ehrhart series is palindromic, thus confirming a related OEIS conjecture.

Contribution

It generalizes Hibi's theorem to a broader class of polytopes associated with bipartite graphs, establishing palindromicity of their Ehrhart series numerator.

Findings

Proved palindromicity for bipartite graph polytopes

Confirmed a conjecture from OEIS

Extended the class of polytopes with palindromic Ehrhart series

Abstract

Hibi showed that the polynomial in the numerator of the Ehrhart series of a reflexive polytope is palindromic. We proved that those in the numerator of the Ehrhart series of every graph polytope (defined later) of the bipartite graph is palindromic. From this, one of the conjectures (raised in the A205497 of OEIS \cite{[O]}) follows immediately.