Inequalities and Ehrhart $\delta$-Vectors
By A. Stapledon. 2008
57 citations recorded by the source corpus.
For any lattice polytope $P$, we consider an associated polynomial $\bar{\delta}_{P}(t)$ and describe its decomposition into a sum of two polynomials satisfying certain symmetry conditions. As a consequence, we improve upon known inequalities satisfied by the coefficients of the Ehrhart $\delta$-vector of a lattice polytope. We also provide combinatorial proofs of two results of Stanley that were previously established using techniques from commutative algebra. Finally, we give a necessary numerical criterion for the existence of a regular unimodular lattice triangulation of the boundary of a lattice polytope.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/53615247129edcefdc4c11ab2a6b3a4fd2c8369a
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
Citations in the corpus
- On the log-concavity of Hilbert series of Veronese subrings and Ehrhart series (2008, background): “We will need the following lemmas, the first of which is motivated by similar results in [ 23 ].”