Some remarkable combinatorial matrices

Abstract

In this paper we describe, in combinatorial terms, some matrices which arise as Laplacians connected to the three-dimensional Heisenberg Lie algebra. We pose the problem of finding the eigenvalues and eigenvectors of these matrices. We state a number of conjectures including the conjecture that all eigenvalues of these matrices are non-negative integers. We determine the eigenvalues and eigenvectors explicitly for an important subclass of these matrices.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30178/1/0000563.pd