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Variations on the Theorem of Birkhoff – von Neumann and Extensions

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Abstract.

 The theorem of Birkhoff – von Neumann concerns bistochastic matrices (i.e., matrices with nonnegative real entries such that all row sums and all column sums are equal to one). We consider here real matrices with entries unrestricted in sign and we extend the notion of permutation matrices (integral bistochastic matrices); some generalizations of the theorem are derived by using elementary properties of graph theory.

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  1. Institut de Mathematiques, Ecole Polytechnique Fédérale de Lausanne, MA-Ecublens, CH-1015 Lausanne, Switzerland. e-mail: dewerra.ima@epfl.ch, , , , , , CH

    Dominique de Werra

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  1. Dominique de Werra
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Received: October 10, 2000 Final version received: April 11, 2002

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de Werra, D. Variations on the Theorem of Birkhoff – von Neumann and Extensions. Graphs and Combinatorics 19, 263–278 (2003). https://doi.org/10.1007/s00373-002-0496-6

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  • DOI: https://doi.org/10.1007/s00373-002-0496-6

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