Homology of generalized partition posets
Algebraic Topology
2011-03-31 v3 Combinatorics
Abstract
We define a poset of partitions associated to an operad. We prove that the operad is Koszul if and only if the poset is Cohen-Macaulay. In one hand, this characterisation allows us to compute the homology of the poset. This homology is given by the Koszul dual operad. On the other hand, we get new methods for proving that an operad is Koszul.
Cite
@article{arxiv.math/0405312,
title = {Homology of generalized partition posets},
author = {Bruno Vallette},
journal= {arXiv preprint arXiv:math/0405312},
year = {2011}
}
Comments
Final version. To appear in JPAA