Membership criteria and containments of powers of monomial ideals

Abstract

We present a close relationship between matching number, covering numbers and their fractional versions in combinatorial optimization and ordinary powers, integral closures of powers, and symbolic powers of monomial ideals. This relationship leads to several new results and problems on the containments between these powers.

25 pages, 2 figures

References in corpus (2)

• Perfectoid multiplier/test ideals in regular rings and bounds on symbolic powers
• Integral closures of monomial ideals and Fulkersonian hypergraphs

Cited by in corpus (5)

• Expected resurgences and symbolic powers of ideals
• Rees algebras of filtrations of covering polyhedra and integral closure of powers of monomial ideals
• Consequences of the packing problem
• Symbolic powers of certain cover ideals of graphs
• Symbolic powers of multipartite hypergraphs and Waldschmidt constant