Powers of squarefree monomial ideals and combinatorics [article]

Christopher A. Francisco, Huy Tai Ha, Jeffrey Mermin
2013 arXiv   pre-print
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
more » ... tion of when symbolic and ordinary powers of squarefree monomial ideals coincide.
arXiv:1303.6642v1 fatcat:6idvqnv2nrfrfkou6b6yusmkgi