7 research outputs found

    A short proof of Minc's conjecture

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    AbstractA short proof is given of the following conjecture of Minc, proved in 1973 by Brègman. Let A be a n × n − (0, 1)-matrix with ri ones in row i. Then per A ⩽ πi=1nri!1ri

    Bounds on the number of eulerian orientations

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    Some remarks on the permanents of circulant (0,1) matrices

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    Some permanents of circulant (0,1) matrices are computed. Three methods are used. First, the permanent of a Kronecker product is computed by directly counting diagonals. Secondly, Lagrange expansion is used to calculate a recurrence for a family of sparse circulants. Finally, a complement expansion method is used to calculate a recurrence for a permanent of a circulant with few zero entries. Also, a bound on the number of different permanents of circulant matrices with a given row sum is obtained

    Bounds on permanents, and the number of 1-factors and 1-factorizations in bipatite graphs

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    The optimal country's policy to attract an MNC new production plant

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