Cellular resolutions of cointerval ideals
Commutative Algebra
2010-04-21 v2 Combinatorics
Abstract
Minimal cellular resolutions of the edge ideals of cointerval hypergraphs are constructed. This class of d-uniform hypergraphs coincides with the complements of interval graphs (for the case d=2), and strictly contains the class of `strongly stable' hypergraphs corresponding to pure shifted simplicial complexes. The polyhedral complexes supporting the resolutions are described as certain spaces of directed graph homomorphisms, and are realized as subcomplexes of mixed subdivisions of the Minkowski sums of simplices. Resolutions of more general hypergraphs are obtained by considering decompositions into cointerval hypergraphs.
Cite
@article{arxiv.1004.0713,
title = {Cellular resolutions of cointerval ideals},
author = {Anton Dochtermann and Alexander Engstrom},
journal= {arXiv preprint arXiv:1004.0713},
year = {2010}
}
Comments
23 pages, 11 figures. Minor revisions and corrections, title slightly modified.