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Unimodular covers of 3-dimensional parallelepipeds and Cayley sums

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arxiv 1907.12312 v1 pith:6EARSO3C submitted 2019-07-29 math.CO

Giulia Codenotti , Francisco Santos This is my paper · ORCID
classification math.CO
keywords classcayleyclassescoversparallelepipedspolytopessumsunimodular
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abstract

We show that the following classes of lattice polytopes have unimodular covers, in dimension three: the class of parallelepipeds, the class of centrally symmetric polytopes, and the class of Cayley sums $\text{Cay}(P,Q)$ 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.

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Cited by 1 Pith paper

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  1. The complete classification of empty lattice $4$-simplices

    math.CO 2019-08 conditional novelty 8.0 of 10

    Every empty lattice 4-simplex belongs to one of 49 infinite families or to one of 2461 sporadic simplices with volume at most 419, completing a 30-year classification program.

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