Hall exponents of matrices, tournaments and their line digraphs
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Let A be a square (0, 1)-matrix. Then A is a Hall matrix provided it has a nonzero permanent. The Hall exponent of A is the smallest positive integer k, if such exists, such that A k is a Hall matrix. The Hall exponent has received considerable attention, and we both review and expand on some of its properties. Viewing A as the adjacency matrix of a digraph, we prove several properties of the Hall exponents of line digraphs with some emphasis on line digraphs of tournament (matrices).
KeywordsHall matrix Hall exponent irreducible primitive tournament (matrix) line digraph
MSC 201015A15 15B34 05C20
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