The Ehrhart quasipolynomial of a rational polytope P encodes the number of integer lattice points in dilates of P, and the h*-polynomial of P is the numerator of the accompanying generating function. We provide two decomposition formulas for the h*-polynomial of a rational polytope. The first decomposition generalizes a theorem of Betke and McMullen for lattice polytopes. We use our rational Betke–McMullen formula to provide a novel proof of Stanley’s Monotonicity Theorem for the h*-polynomial of a rational polytope. The second decomposition generalizes a result of Stapledon, which we use to provide rational extensions of the Stanley and Hibi inequalities satisfied by the coefficients of the h*-polynomial for lattice polytopes. Lastly, we apply our results to rational polytopes containing the origin whose duals are lattice polytopes.
|Journal||Seminaire Lotharingien de Combinatoire|
|State||Published - 2021|
Bibliographical noteFunding Information:
*email@example.com. Andrés R. Vindas-Meléndez was partially supported by National Science Foundation Graduate Research Fellowship DGE-1247392.
© 2021, Seminaire Lotharingien de Combinatoire. All Rights Reserved.
- Ehrhart quasipolynomial
- Ehrhart series
- generating function
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics