Hanusa, Christopher R. H.; Zaslavsky, Thomas Determinants in the Kronecker product of matrices: the incidence matrix of a complete graph. (English) Zbl 1218.15003 Linear Multilinear Algebra 59, No. 4, 399-411 (2011). Summary: We investigate the least common multiple of all subdeterminants, lcmd\((A \otimes B)\), 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 \(A\). Cited in 1 Document MSC: 15A15 Determinants, permanents, traces, other special matrix functions 11A05 Multiplicative structure; Euclidean algorithm; greatest common divisors 05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.) 15B36 Matrices of integers 15A69 Multilinear algebra, tensor calculus 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) Keywords:least common multiple; subdeterminants; Kronecker product; integral matrix; incidence matrix; complete graph × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] Chaiken S, A q-queens problem [2] Horn RA, Topics in Matrix Analysis (1991) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.