与代数统计相关的锥的Hilbert基的迭代计算
Challenging computations of Hilbert bases of cones associated with algebraic statistics
摘要：
本文给出了由$5\times 5\times 3$列联表导出的幺半群正规的两个独立的计算证明，完成了Hibi和Ohsugi的分类.我们表明，Vlach的向量反证正规性的幺半群来自$6\times 4\times 3$列联表是唯一的最小这样的向量对称。最后，我们计算了$|N|=5$的半图面的非正规幺半群所对应的锥的全Hilbert基。这些计算基于LattE-4 ti 2和Normaliz包的扩展。
英文摘要：
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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