Sortable simplicial complexes and $t$-independence ideals of proper interval graphs
Commutative Algebra
2019-08-21 v1
Abstract
We introduce the notion of sortability and -sortability for a simplicial complex and study the graphs for which their independence complexes are either sortable or -sortable. We show that the proper interval graphs are precisely the graphs whose independence complex is sortable. By using this characterization, we show that the ideal generated by all squarefree monomials corresponding to independent sets of vertices of of size (for a given positive integer ) has the strong persistence property, when is a proper interval graph. Moreover, all of its powers have linear quotients.
Cite
@article{arxiv.1908.07179,
title = {Sortable simplicial complexes and $t$-independence ideals of proper interval graphs},
author = {Jürgen Herzog and Fahimeh Khosh-Ahang and Somayeh Moradi and Masoomeh Rahimbeigi},
journal= {arXiv preprint arXiv:1908.07179},
year = {2019}
}