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Advances in Discrete Tomography and Its Applications pp 113–123Cite as

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

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Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

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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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin Madison, Wisconsin, 53706, USA

    R.A. Brualdi

  2. Center of Mathematics for Applications, University of Oslo, P.O. Box1053, Blindern, NO-0316 Oslo, Norway

    G. Dahl

Authors
  1. R.A. Brualdi
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  2. G. Dahl
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Editor information

Editors and Affiliations

  1. Program in Computer Science The Graduate Center, The City University of New York, 365 Fifth Avenue, New York, NY, 10016, USA

    Gabor T. Herman

  2. Department of Image Processing and Computer Graphics, University of Szeged, Árpád tér 2 H-6720 , Szeged, Hungary

    Attila Kuba

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© 2007 Birkhäuser Boston

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Brualdi, R., Dahl, G. (2007). Constructing (0,1)-Matrices with Given Line Sums and Certain Fixed Zeros. In: Herman, G.T., Kuba, A. (eds) Advances in Discrete Tomography and Its Applications. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4543-4_6

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  • DOI: https://doi.org/10.1007/978-0-8176-4543-4_6

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-0-8176-3614-2

  • Online ISBN: 978-0-8176-4543-4

  • eBook Packages: EngineeringEngineering (R0)

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