 
Summary: journal of combinatorial theory, Series A 73, 360 367 (1996)
Note
On Hanlon's Eigenvalue Conjecture
R. M. Adin*
Department of Mathematics and Computer Science, BarIlan University,
RamatGan 52900, Israel
and
C. A. Athanasiadis
Department of Mathematics, Massachusetts Institute of Technology,
Cambridge, Massachusetts 02139
Communicated by GianCarlo Rota
Received January 13, 1995
P. Hanlon (J. Combin. Theory Ser. A 59 (1992), 218 239) has conjectured an
explicit formula for the eigenvalues of certain combinatorial matrices related to the
cohomology of nilpotent Lie algebras. Several special cases of this conjecture are
now established. 1996 Academic Press, Inc.
1. Introduction
Let Gk(a, b) be the disjoint union of the graphs Gk(a, b; w), introduced
in [H], for all possible w. Recall that if
Mk(x, y, *)= :
