Homology of matching complexes and representations of symmetric groups
Abstract
We compute the homology of the matching complex M ( Γ ) M(\Gamma ) , where Γ \Gamma is the complete hypergraph on n ≥ 2 n\geq 2 vertices, and then analyse the S n S_{n} -representations carried by this homology. These results are achieved using standard techniques in combinatorial topology, such as the theory of shellings. We then broaden the scope to the larger class of fibre-closed families of simplicial complexes and consider these through the lens of representation stability. This allows us to prove a number of results of an asymptotic nature, such as an analysis of the growth of Betti numbers and the kinds of irreducible S n S_n -representations that appear.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Commutative Algebra and Its Applications
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 4
- Pages
- 1467–1478
- Publication date
- 10 February 2026
- Language
- EN