 
Summary: On Hanlon's Eigenvalue Conjecture
R. M. Adin \Lambda
Department of Mathematics and Computer Science
BarIlan University
RamatGan 52900, ISRAEL
radin@bimacs.cs.biu.ac.il
C. A. Athanasiadis
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA 02139, USA
cathan@math.mit.edu
Version of January 13, 1995
Abstract
P. Hanlon [J. Combin. Theory, series A 59 (1992), 218239] 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.
1 Introduction
Let G k (a; b) be the disjoint union of the graphs G k (a; b; w), introduced in [H], for all
possible w. Recall that if
