Parity binomial edge ideals
Commutative Algebra
2017-02-15 v3 Combinatorics
Abstract
Parity binomial edge ideals of simple undirected graphs are introduced. Unlike binomial edge ideals, they do not have square-free Gr\"obner bases and are radical if only if the graph is bipartite or the characteristic of the ground field is not two. The minimal primes are determined and shown to encode combinatorics of even and odd walks in the graph. A mesoprimary decomposition is determined and shown to be a primary decomposition in characteristic two.
Cite
@article{arxiv.1503.00584,
title = {Parity binomial edge ideals},
author = {Thomas Kahle and Camilo Sarmiento and Tobias Windisch},
journal= {arXiv preprint arXiv:1503.00584},
year = {2017}
}
Comments
21 pages, 3 figures, v2: minor problem in proof of Lemma 2.4 corrected, construction of Gr\"obner basis in Section 3 corrected, Example 5.1 replaced by Remark 5.1, final version as in Journal of Algebraic Combinatorics, v3: footnote to Lemma 3.8 added