Ehrhart-equivalent 3-polytopes are equidecomposable

Erbe, Jakob; Haase, Christian; Santos, Francisco

doi:10.1090/proc/14626

Ehrhart-equivalent $\boldsymbol 3$-polytopes are equidecomposable
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by Jakob Erbe, Christian Haase and Francisco Santos PDF

Proc. Amer. Math. Soc. 147 (2019), 5373-5383 Request permission

Abstract:

We show that if two lattice $3$-polytopes $P$ and $P’$ have the same Ehrhart function, then they are $\operatorname {GL}_d(\mathbb {Z})$-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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