Linear decision trees: volume estimates and topological bounds
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Regular Article: Foundations of a Connectivity Theory for Simplicial Complexes
Advances in Applied Mathematics
Journal of Algebraic Combinatorics: An International Journal
| Hi-index | 0.00 |
In a previous work, we defined a family of subcomplexes of the n-dimensional half cube by removing the interiors of all half cube shaped faces of dimension at least k, and we proved that the reduced homology of such a subcomplex is concentrated in degree k-1. This homology module supports a natural action of the Coxeter group W(D"n) of type D. In this paper, we explicitly determine the characters (over C) of these homology representations, which turn out to be multiplicity free. Regarded as representations of the symmetric group S"n by restriction, the homology representations turn out to be direct sums of certain representations induced from parabolic subgroups. The latter representations of S"n agree (over C) with the representations of S"n on the (k-2)-nd homology of the complement of the k-equal real hyperplane arrangement.