Generalized Binomial Edge Ideals
Commutative Algebra
2014-06-18 v1
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 Gr\"obner basis can be computed by studying paths in the graph. Since these Gr\"obner 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.
Cite
@article{arxiv.1210.7960,
title = {Generalized Binomial Edge Ideals},
author = {Johannes Rauh},
journal= {arXiv preprint arXiv:1210.7960},
year = {2014}
}
Comments
6 pages. arXiv admin note: substantial text overlap with arXiv:1110.1338