Chorded complexes and a necessary condition for a monomial ideal to have a linear resolution

Abstract

In this paper we extend one direction of Fröberg's 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 also give a necessary combinatorial condition for a monomial ideal to be componentwise linear over all fields.

Revised to appear in Journal of Combinatorial Theory, Series A

References in corpus (2)

• Monomial ideals with 3-linear resolutions
• On $d$-dimensional cycles and the vanishing of simplicial homology

Cited by in corpus (1)

• The Betti numbers of Stanley-Reisner ideals of simplicial trees