Minimal primes of ideals arising from conditional independence statements

Details Minimal primes of ideals arising from conditional independence statements Minimal primes of ideals arising from conditional independence statements

2011-07-27

arxiv.org/abs/1107.5604v4

Mathematics

Commutative Algebra

We shortened and streamlined the paper from 24 to 17 pages, we improved several proofs, we updated references, and we added Gr

Scientific paper

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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