Minimal primes of ideals arising from conditional independence statements

Irena Swanson; Amelia Taylor

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arXiv · 1107.5604

Minimal primes of ideals arising from conditional independence statements

Irena Swanson·Amelia Taylor

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Abstract

We consider ideals arising in the context of conditional independence models that generalize the class of ideals considered by Fink [7] in a way distinct from the generalizations of Herzog-Hibi-Hreinsdottir-Kahle-Rauh [13] and Ay-Rauh [1]. We introduce switchable sets to give a combinatorial description of the minimal prime ideals, and for some classes we describe the minimal components. We discuss many possible interpretations of the ideals we study, including as 2 \times 2 minors of generic hypermatrices. We also introduce a definition of diagonal monomial orders on generic hypermatrices and we compute some Groebner bases.

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Irena Swanson, Amelia Taylor. 2012-04-11. Minimal primes of ideals arising from conditional independence statements. https://arxiv.org/abs/1107.5604

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