Ehrhart-equivalent $3$-polytopes are equidecomposable

Abstract

We show that if two lattice $3$-polytopes $P$ and $P^{\prime }$ have the same Ehrhart function then they are ${\mathrm{GL}}_3(\mathbb{Z})$-equidecomposable; that is, they can be partitioned into relatively open simplices $U_1,\dots ,U_k$ and $U_1^{\prime },\dots ,U_k^{\prime }$ such that $U_i$ and $U_i^{\prime }$ are unimodularly equivalent, for each $i$.

11 pages

References in corpus (3)

• Existence of unimodular triangulations - positive results
• Quasi-period collapse and GL_n(Z)-scissors congruence in rational polytopes
• Conditions for Discrete Equidecomposability of Polygons

Cited by in corpus (2)

• Chainlink Polytopes and Ehrhart-Equivalence
• Ehrhart-Equivalence, Equidecomposability, and Unimodular Equivalence of Integral Polytopes