Name
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. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.ejc.2012.10.005 | Eur. J. Comb. |
Keywords | Field | DocType |
special case,squarefree monomial ideal,monomial ideal,well-known characterization,new class,polymatroidal ideal,componentwise polymatroidal ideal,monomial localization,linear resolution | Matroid,Discrete mathematics,Combinatorics,Square-free integer,If and only if,Monomial ideal,Monomial,Conjecture,Mathematics | Journal |
Volume | Issue | ISSN |
34 | 4 | 0195-6698 |
Citations | PageRank | References |
1 | 0.50 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Somayeh Bandari | 1 | 1 | 0.50 |
| Jürgen Herzog | 2 | 28 | 7.98 |