Lattice polytopes having h^*-polynomials with given degree and linear coefficient
Combinatorics
2008-09-29 v2
Abstract
The h^*-polynomial of a lattice polytope is the numerator of the generating function of the Ehrhart polynomial. Let P be a lattice polytope with h^*-polynomial of degree d and with linear coefficient h^*_1. We show that P has to be a lattice pyramid over a lower-dimensional lattice polytope, if the dimension of P is greater or equal to h^*_1 (2d+1) + 4d-1. This result has a purely combinatorial proof and generalizes a recent theorem of Batyrev.
Keywords
Cite
@article{arxiv.0705.1082,
title = {Lattice polytopes having h^*-polynomials with given degree and linear coefficient},
author = {Benjamin Nill},
journal= {arXiv preprint arXiv:0705.1082},
year = {2008}
}