Splittable ideals and the resolutions of monomial ideals

Citations of this article
Mendeley users who have this article in their library.


We provide a new combinatorial approach to study the minimal free resolutions of edge ideals, that is, quadratic square-free monomial ideals. With this method we can recover most of the known results on resolutions of edge ideals with fuller generality, and at the same time, obtain new results. Past investigations on the resolutions of edge ideals usually reduced the problem to computing the dimensions of reduced homology or Koszul homology groups. Our approach circumvents the highly nontrivial problem of computing the dimensions of these groups and turns the problem into combinatorial questions about the associated simple graph. We also show that our technique extends successfully to the study of graded Betti numbers of arbitrary square-free monomial ideals viewed as facet ideals of simplicial complexes. © 2006 Elsevier Inc. All rights reserved.




Hà, H. T., & Van Tuyl, A. (2007). Splittable ideals and the resolutions of monomial ideals. Journal of Algebra, 309(1), 405–425. https://doi.org/10.1016/j.jalgebra.2006.08.022

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free