Name
Title | ||
|---|---|---|
Chorded complexes and a necessary condition for a monomial ideal to have a linear resolution. |
Abstract | ||
|---|---|---|
In this paper we extend one direction of Fröbergʼs theorem on a combinatorial classification of quadratic monomial ideals with linear resolutions. We do this by generalizing the notion of a chordal graph to higher dimensions with the introduction of d-chorded and orientably-d-cycle-complete simplicial complexes. We show that a certain class of simplicial complexes, the d-dimensional trees, correspond to ideals having linear resolutions over fields of characteristic 2 and we also give a necessary combinatorial condition for a monomial ideal to be componentwise linear over all fields. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.jcta.2013.05.009 | Journal of Combinatorial Theory, Series A |
Keywords | Field | DocType |
Linear resolution,Monomial ideal,Chordal graph,Simplicial complex,Simplicial homology,Stanley–Reisner complex,Facet complex,Chordal hypergraph | Discrete mathematics,Betti number,Combinatorics,Simplicial approximation theorem,Simplicial homology,Simplicial complex,h-vector,Monomial ideal,Monomial,Mathematics,Abstract simplicial complex | Journal |
Volume | Issue | ISSN |
120 | 7 | 0097-3165 |
Citations | PageRank | References |
3 | 0.72 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Emma L. Connon | 1 | 9 | 1.34 |
| Sara Faridi | 2 | 10 | 3.13 |