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arXiv · 1807.09485

Ehrhart-equivalent $\boldsymbol 3$-polytopes are equidecomposable

Jakob Erbe·Christian Haase·Francisco Santos
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Abstract

We show that if two lattice $3$-polytopes $P$ and $P'$ have the same Ehrhart function then they are $\operatorname{GL}_3({\mathbb Z})$-equidecomposable; that is, they can be partitioned into relatively open simplices $U_1,\dots, U_k$ and $U'_1,\dots,U'_k$ such that $U_i$ and $U'_i$ are unimodularly equivalent, for each $i$.

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Jakob Erbe, Christian Haase, Francisco Santos. 2018-07-25. Ehrhart-equivalent $\boldsymbol 3$-polytopes are equidecomposable. https://doi.org/10.1090/proc%2F14626

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