English

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 hh-vector for all the toric ideals of graphs in this family.

Keywords

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