2011/07/27 by Irena Swanson, Swanson, Irena, Amelia Taylor +1 · 1 citation
Computer Science · Mathematics · #13P10 #13P25 #Advanced Combinatorial Mathematics #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1107.5604
openalex publication_date 2011/07/27 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We consider ideals arising in the context of conditional independence models\nthat generalize the class of ideals considered by Fink [7] in a way distinct\nfrom the generalizations of Herzog-Hibi-Hreinsdottir-Kahle-Rauh [13] and\nAy-Rauh [1]. We introduce switchable sets to give a combinatorial description\nof the minimal prime ideals, and for some classes we describe the minimal\ncomponents. We discuss many possible interpretations of the ideals we study,\nincluding as 2 \× 2 minors of generic hypermatrices. We also introduce a\ndefinition of diagonal monomial orders on generic hypermatrices and we compute\nsome Groebner bases.\n