Ehrhart series and lattice triangulations
Sam Payne
TL;DR
This paper develops a method to express the generating function for lattice points in rational polyhedral cones using multivariate h-polynomials and local contributions, and presents new examples of nonunimodal h^*-vectors of reflexive polytopes.
Contribution
It introduces a novel formula connecting lattice point generating functions with multivariate h-polynomials and local contributions, and provides new examples of nonunimodal h^*-vectors.
Findings
Derived a new expression for lattice point generating functions.
Computed examples of nonunimodal h^*-vectors.
Enhanced understanding of the structure of reflexive polytopes.
Abstract
We express the generating function for lattice points in a rational polyhedral cone with a simplicial subdivision in terms of multivariate analogues of the h-polynomials of the subdivision and "local contributions" of the links of its nonunimodular faces. We also compute new examples of nonunimodal h^*-vectors of reflexive polytopes.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Mathematical Identities · Algebraic Geometry and Number Theory