Monomial localizations and polymatroidal ideals

Authors:
Somayeh Bandari;JüRgen Herzog
Affiliations:
Department of Mathematics, Az-Zahra University, Vanak, Post Code 19834, Tehran, Iran;Fachbereich Mathematik, Universität Duisburg-Essen, Campus Essen, 45117 Essen, Germany
Venue:
European Journal of Combinatorics
Year:
2013

Citing 2
Cited 0

Note: Ideals with linear quotients

Journal of Combinatorial Theory Series A
The stable set of associated prime ideals of a polymatroidal ideal

Journal of Algebraic Combinatorics: An International Journal

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Abstract

In this paper we consider monomial localizations of monomial ideals and conjecture that a monomial ideal is polymatroidal if and only if all its monomial localizations have a linear resolution. The conjecture is proved for squarefree monomial ideals where it is equivalent to a well-known characterization of matroids. We prove our conjecture in many other special cases. We also introduce the concept of componentwise polymatroidal ideals and extend several of the results known for polymatroidal ideals to this new class of ideals.