Determinants in the Kronecker product of matrices: The incidence matrix of a complete graph

Abstract

We investigate the least common multiple of all subdeterminants, lcmd(A x B), of a Kronecker product of matrices, of which one is an integral matrix A with two columns and the other is the incidence matrix of a complete graph with n vertices. We prove that this quantity is the least common multiple of lcmd(A) to the power n-1 and certain binomial functions of the entries of A.

arXiv comment15 pages, 2 figures; revised and updated version to appear in Linear and Multilinear Algebra, 2010