Combinatorial Laplacian of the Matching Complex

  • Xun Dong
  • Michelle L. Wachs

Abstract

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.

Published
2002-04-02
Article Number
R17