Homology of the Boolean Complex

Details Homology of the Boolean Complex Homology of the Boolean Complex

2010-05-24

arxiv.org/abs/1005.4411v2

Mathematics

Combinatorics

final version, to appear in Journal of Algebraic Combinatorics

Scientific paper

We construct and analyze an explicit basis for the homology of the boolean complex of a Coxeter system. This gives combinatorial meaning to the spheres in the wedge sum describing the homotopy type of the complex. We assign a set of derangements to any finite simple graph. For each derangement, we construct a corresponding element in the homology of the complex, and the collection of these elements forms a basis for the homology of the boolean complex. In this manner, the spheres in the wedge sum describing the homotopy type of the complex can be represented by a set of derangements. We give an explicit, closed-form description of the derangements that can be obtained from any graph, and compute this set for several families of graphs. In the cases of complete graphs and Ferrers graphs, these calculations give bijective proofs of previously obtained enumerative results.

Affiliated with

Also associated with

No associations

Rating

Homology of the Boolean Complex does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Homology of the Boolean Complex, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Homology of the Boolean Complex will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-296753