An ehrhart series formula for reflexive polytopes

Benjamin Braun

doi:10.37236/1153

An ehrhart series formula for reflexive polytopes

Benjamin Braun

Mathematics

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

It is well known that for P and Q lattice polytopes, the Ehrhart polynomial of PxQ satisfies L_PxQ(t) = L_P (t)L_Q(t). We show that there is a similar multiplicative relationship between the Ehrhart series for P, for Q, and for the free sum P ⊕ Q that holds when P is reflexive and Q contains 0 in its interior.

Original language	English
Pages (from-to)	1-5
Number of pages	5
Journal	Electronic Journal of Combinatorics
Volume	13
Issue number	1 N
DOIs	https://doi.org/10.37236/1153
State	Published - Oct 5 2006

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

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10.37236/1153

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abstract = "It is well known that for P and Q lattice polytopes, the Ehrhart polynomial of PxQ satisfies LPxQ(t) = LP (t)LQ(t). We show that there is a similar multiplicative relationship between the Ehrhart series for P, for Q, and for the free sum P ⊕ Q that holds when P is reflexive and Q contains 0 in its interior.",

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AB - It is well known that for P and Q lattice polytopes, the Ehrhart polynomial of PxQ satisfies LPxQ(t) = LP (t)LQ(t). We show that there is a similar multiplicative relationship between the Ehrhart series for P, for Q, and for the free sum P ⊕ Q that holds when P is reflexive and Q contains 0 in its interior.

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An ehrhart series formula for reflexive polytopes

Abstract

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