Combinatorial Laplacian of the Matching Complex
Xun Dong, Michelle L. Wachs · The Electronic Journal of Combinatorics · 2002
A striking result of Bouc gives the decomposition of the representation of the symmetric group on the homology of the matching complex into irreducibles that are self-conjugate. We show how the combinatorial Laplacian can be used to give an elegant proof of this result. We also show that the spectrum of the Laplacian is integral.