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

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

2008-11-12

arxiv.org/abs/0811.1930v2

Mathematics

Combinatorics

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

Scientific paper

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.

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