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arXiv · 1001.4145

Challenging computations of Hilbert bases of cones associated with algebraic statistics

Winfried Bruns·Raymond Hemmecke·Bogdan Ichim·Matthias Koeppe·Christof Soeger
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Abstract

In this paper we present two independent computational proofs that the monoid derived from $5\times 5\times 3$ contingency tables is normal, completing the classification by Hibi and Ohsugi. We show that Vlach's vector disproving normality for the monoid derived from $6\times 4\times 3$ contingency tables is the unique minimal such vector up to symmetry. Finally, we compute the full Hilbert basis of the cone associated with the non-normal monoid of the semi-graphoid for $|N|=5$. The computations are based on extensions of the packages LattE-4ti2 and Normaliz.

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Winfried Bruns, Raymond Hemmecke, Bogdan Ichim, Matthias Koeppe, Christof Soeger. 2010-01-23. Challenging computations of Hilbert bases of cones associated with algebraic statistics. https://arxiv.org/abs/1001.4145

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