余维2中的强鲁棒环面理想

Journal of Algebraic Statistics Pub Date : 2016-10-24 DOI:10.18409/JAS.V10I1.62

S. Sullivant

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引用次数: 10

摘要

齐次理想是鲁棒的，如果它的全称Gröbner基也是一个极小的发电集。对于环理想，有一个更强的定义:一个环理想是强鲁棒的，如果它的格拉弗基等于一组不可或缺的二项。我们用Gale图刻画了余维2强鲁棒环理想。这就给了Petrovic, Thoma和Vladoiu关于余维数为2的环面理想的问题一个肯定的答案。

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Strongly Robust Toric Ideals in Codimension 2

A homogeneous ideal is robust if its universal Gröbner basis is also a minimal generating set. For toric ideals, one has the stronger definition: A toric ideal is strongly robust if its Graver basis equals the set of indispensable binomials. We characterize the codimension 2 strongly robust toric ideals by their Gale diagrams. This give a positive answer to a question of Petrovic, Thoma, and Vladoiu in the case of codimension 2 toric ideals.

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Journal of Algebraic Statistics STATISTICS & PROBABILITY-

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