Constructing (0,1)-Matrices with Given Line Sums and Certain Fixed Zeros

  • R.A. Brualdi
  • G. Dahl
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


Consider the class AP(R, S) of (0, 1)-matrices with row sum vector R, column sum vector S, and zeros in all positions outside a certain set P. It is assumed that P satisfies a certain monotonicity property. We show the existence of a canonical matrix in this matrix class and give a simple algorithm for finding this matrix. Moreover, a classical interchange result of Ryser is generalized to the class AP(R, S) and the uniqueness question for the class AP(R, S) is discussed.


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Copyright information

© Birkhäuser Boston 2007

Authors and Affiliations

  • R.A. Brualdi
    • 1
  • G. Dahl
    • 2
  1. 1.Department of MathematicsUniversity of Wisconsin MadisonWisconsinUSA
  2. 2.Center of Mathematics for Applications, University of OsloBlindernNorway

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