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arXiv · 1304.2498

Closure of principal L-type domain and its parallelotopes

Mathieu Dutour Sikiric·Viacheslav Grishukhin
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Abstract

Voronoi defined two polyhedral partitions of the cone of se\mi\de\fi\nite forms into L-type domains and into perfect domains. Up to equivalence, there is only one domain that is simultaneously perfect and L-type. Voronoi called this domain {\em principal}. We show that closure of the principal domain may be identified with a cone of cut submodular set functions. Parallelotopes of the closed principal domain are zonotopes that are base polyhedra related to graphic unimodular sets of vectors.

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Mathieu Dutour Sikiric, Viacheslav Grishukhin. 2013-04-09. Closure of principal L-type domain and its parallelotopes. https://arxiv.org/abs/1304.2498

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