Details:
Title  Minimal primes of ideals arising from conditional independence statements  Author(s)  Irena Swanson, Amelia Taylor  Type  Article in Journal  Abstract  Abstract We study ideals whose primary decomposition specifies the relevant structural zeros of certain conditional independence models. The ideals we study generalize the class of ideals considered by Fink (2011) [5] in a way distinct from the generalizations of Herzog, Hibi, Hreinsdottir, Kahle, and Rauh (2010) [10] and Ay and Rauh (2011) [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 possible interpretations of the ideals we study, including as 2 × 2 minors of generic hypermatrices. We also introduce a definition of diagonal monomial orders on generic hypermatrices to compute some Gröbner bases.  Keywords  Primary decomposition, Conditional independence ideals, Graphical models, Gróbner bases, Binomial ideals  ISSN  00218693 
URL 
http://www.sciencedirect.com/science/article/pii/S0021869313003049 
Language  English  Journal  Journal of Algebra  Volume  392  Pages  299  314  Year  2013  Edition  0  Translation 
No  Refereed 
No 
