Journal of Algebraic Combinatorics

, Volume 8, Issue 2, pp 193–203

On the Betti Numbers of Chessboard Complexes

Authors

  • Joel Friedman
    • Department of MathematicsUniversity of British Columbia
  • Phil Hanlon
    • Department of MathematicsUniversity of Michigan
Article

DOI: 10.1023/A:1008693929682

Cite this article as:
Friedman, J. & Hanlon, P. Journal of Algebraic Combinatorics (1998) 8: 193. doi:10.1023/A:1008693929682

Abstract

In this paper we study the Betti numbers of a type of simplicial complex known as a chessboard complex. We obtain a formula for their Betti numbers as a sum of terms involving partitions. This formula allows us to determine which is the first nonvanishing Betti number (aside from the 0-th Betti number). We can therefore settle certain cases of a conjecture of Björner, Lovász, Vrećica, and Živaljević in [2]. Our formula also shows that all eigenvalues of the Laplacians of the simplicial complexes are integers, and it gives a formula (involving partitions) for the multiplicities of the eigenvalues.

chessboard complexLaplaciansymmetric grouprepresentationconnectivityBetti number

Copyright information

© Kluwer Academic Publishers 1998