Year: 2012
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Bandari, Somayeh, Herzog, Jürgen
Institutions: Alzahra University, University of Duisburg-Essen
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952854636