Reconstruction of symmetric convex bodies from Ehrhart-like data

Abstract

In a previous paper, we showed how to use the Ehrhart function $L_P(s)$, defined by $L_P(s)=\#(sP\cap {\mathbb{Z}}^d)$, to reconstruct a polytope $P$. More specifically, we showed that, for rational polytopes $P$ and $Q$, if $L_{P+w}(s)=L_{Q+w}(s)$ for all integer vectors $w$, then $P=Q$. In this paper we show the same result, but assuming that $P$ and $Q$ are symmetric convex bodies instead of rational polytopes.

References in corpus (1)

• Reconstruction of rational polytopes from the real-parameter Ehrhart function of its translates