Betti numbers of toric ideals of graphs: A case study
Commutative Algebra
2019-11-12 v2 Combinatorics
Abstract
We compute the graded Betti numbers for the toric ideal of a family of graphs constructed by adjoining a cycle to a complete bipartite graph. The key observation is that this family admits an initial ideal which has linear quotients. As a corollary, we compute the Hilbert series and -vector for all the toric ideals of graphs in this family.
Cite
@article{arxiv.1807.02154,
title = {Betti numbers of toric ideals of graphs: A case study},
author = {Federico Galetto and Johannes Hofscheier and Graham Keiper and Craig Kohne and Miguel Eduardo Uribe Paczka and Adam Van Tuyl},
journal= {arXiv preprint arXiv:1807.02154},
year = {2019}
}
Comments
12 pages; revised and corrected; to appear in Journal of Algebra and its Applications