Generalized Binomial Edge Ideals

Abstract

This paper studies a class of binomial ideals associated to graphs with finite vertex sets. They generalize the binomial edge ideals, and they arise in the study of conditional independence ideals. A Gröbner basis can be computed by studying paths in the graph. Since these Gröbner bases are square-free, generalized binomial edge ideals are radical. To find the primary decomposition a combinatorial problem involving the connected components of subgraphs has to be solved. The irreducible components of the solution variety are all rational.

6 pages. arXiv admin note: substantial text overlap with arXiv:1110.1338

References in corpus (2)

• Robustness, Canalyzing Functions and Systems Design
• Minimal primes of ideals arising from conditional independence statements

Cited by in corpus (10)

• Prime splittings of Determinantal Ideals
• Robustness, Canalyzing Functions and Systems Design
• Positive margins and primary decomposition
• On closed graphs II
• Weakly closed graphs and F-purity of binomial edge ideals
• Conditional independence ideals with hidden variables
• On a regularity-conjecture of generalized binomial edge ideals
• Ideals generated by $2$--minors of Hankel matrices
• F-Purity of Binomial Edge Ideals
• On The Generalized Binomial Edge Ideals of Generalized Block Graphs