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 nonnormal monoid of the semigraphoid for |N|=5. The computations are based on extensions of the packages LattE-4ti2and Normaliz.
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