Even and odd diagonals in doubly stochastic matrices |
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Authors: | Joachim von Below Simon Rénier |
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Institution: | LMPA Joseph Liouville, EA 2597 FCNRS, Université du Littoral Côte d’Opale, 50, rue F. Buisson, B.P. 699, F-62228 Calais Cedex, France |
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Abstract: | The existence of even or odd diagonals in doubly stochastic matrices depends on the number of positive elements in the matrix. The optimal general lower bound in order to guarantee the existence of such diagonals is determined, as well as their minimal number for given number of positive elements. The results are related to the characterization of even doubly stochastic matrices in connection with Birkhoff's algorithm. |
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Keywords: | 15A51 05C50 05D15 |
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