Combinatorial Laplacian of the Matching Complex

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.

• Type: Journal
• Year: 2002
• Where: COMBINATORICS
• Authors: Xun Dong, Michelle L. Wachs
• Keywords: COMBINATORICS 2002, Elegant Proof, Laplacian, Symmetric Group