Powers of squarefree monomial ideals and combinatorics
Commutative Algebra
2013-03-28 v1 Combinatorics
Abstract
We survey research relating algebraic properties of powers of squarefree monomial ideals to combinatorial structures. In particular, we describe how to detect important properties of (hyper)graphs by solving ideal membership problems and computing associated primes. This work leads to algebraic characterizations of perfect graphs independent of the Strong Perfect Graph Theorem. In addition, we discuss the equivalence between the Conforti-Cornuejols conjecture from linear programming and the question of when symbolic and ordinary powers of squarefree monomial ideals coincide.
Cite
@article{arxiv.1303.6642,
title = {Powers of squarefree monomial ideals and combinatorics},
author = {Christopher A. Francisco and Huy Tai Ha and Jeffrey Mermin},
journal= {arXiv preprint arXiv:1303.6642},
year = {2013}
}
Comments
18 pages, 2 figures