Czechoslovak Mathematical Journal

, Volume 61, Issue 2, pp 461–481 | Cite as

Hall exponents of matrices, tournaments and their line digraphs

  • Richard A. Brualdi
  • Kathleen P. Kiernan


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).


Hall matrix Hall exponent irreducible primitive tournament (matrix) line digraph 

MSC 2010

15A15 15B34 05C20 


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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2011

Authors and Affiliations

  1. 1.Madison Department of MathematicsUniversity of WisconsinMadisonUSA

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