Minimum permanents on certain doubly stochastic matrices. II (Q1183159)
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scientific article; zbMATH DE number 32821
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| English | Minimum permanents on certain doubly stochastic matrices. II |
scientific article; zbMATH DE number 32821 |
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Minimum permanents on certain doubly stochastic matrices. II (English)
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28 June 1992
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[For part I see ibid. 143, 49-56 (1991; Zbl 0712.15018).] For certain values of \(m\) and \(n\) the minimum permanents and minimizing matrices over the \((m+n)\times (m+n)\) doubly stochastic matrices whose nonzero entries are the same as those of \[ \left [ \begin{matrix} J_{m,m} & J_{m,n} \\ J_{n,m} & I_ n \end{matrix} \right] \quad\hbox{ or }\quad \left[ \begin{matrix} J_{m,m} & 0_{m-2,n} \\ & J_{2,n} \\ J_{n,m} & I_ n \end{matrix} \right] \] are determined. Each \(J_{\alpha,\beta}\) is an \(\alpha\times \beta\) matrix of ones and \(0_{m-2,n}\) is a \((m-2)\times n\) matrix of zeros; \(I_ n\) is the \(n\times n\) identity matrix.
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minimum permanents
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minimizing matrices
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doubly stochastic matrices
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