Challenging computations of Hilbert bases of cones associated with algebraic statistics

2010/01/23 by Winfried Bruns, Bruns, Winfried, Raymond Hemmecke +7
Mathematics · #13F20 #52B20 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.CO #msc:13F20 #msc:52B20

paper · pdf · doi:10.48550/arxiv.1001.4145

10 pages

arxiv created 2010/01/23 · arxiv updated 2010/02/26

Abstract

In this paper we present two independent computational proofs that the monoid derived from 5× 5× 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× 4× 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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