Betti numbers of cut ideals of trees
Commutative Algebra
2013-10-29 v2 Combinatorics
Abstract
Cut ideals, introduced by Sturmfels and Sullivant, are used in phylogenetics and algebraic statistics. We study the minimal free resolutions of cut ideals of tree graphs. By employing basic methods from topological combinatorics, we obtain upper bounds for the Betti numbers of this type of ideals. These take the form of simple formulas on the number of vertices, which arise from the enumeration of induced subgraphs of certain incomparability graphs associated to the edge sets of trees.
Keywords
Cite
@article{arxiv.1209.6372,
title = {Betti numbers of cut ideals of trees},
author = {Samu Potka and Camilo Sarmiento},
journal= {arXiv preprint arXiv:1209.6372},
year = {2013}
}
Comments
11 pages. Minor revisions