Codenotti, Giulia; Santos, Francisco

doi:10.5070/C63362785

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Unimodular covers of $3$ -dimensional parallelepipeds and Cayley sums

2023

Published Web Location

https://doi.org/10.5070/C63362785

Creative Commons 'BY' version 4.0 license

Abstract

We show that the following classes of lattice polytopes have unimodular covers, in dimension three: parallelepipeds, smooth centrally symmetric polytopes, and Cayley sums $Cay (P, Q)$ where the normal fan of $Q$ refines that of $P$ . This improves results of Beck et al. (2018) and Haase et al. (2008) where the last two classes were shown to be IDP.

Mathematics Subject Classifications: 52B10, 52B20, 52C17

Keywords: Lattice polytopes, unimodular covers, integer decomposition property

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Combinatorial Theory

Unimodular covers of 3-dimensional parallelepipeds and Cayley sums

Published Web Location

Unimodular covers of $3$ -dimensional parallelepipeds and Cayley sums