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Original Articles

Minimum permanents of doubly stochastic matrices with prescribed zero entriesFootnote

Pages 225-243 | Received 29 Nov 1982, Published online: 02 Apr 2008

References

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  • Falikman , D. I. 1981 . Dokazatel'stvo gipotezy van der Vardena o permanente dva[zcirc]dy stohastiĉeskoî matricy . Mat. Zam. , 29 ( 45 ) : 931 – 938 .
  • London , David . 1971 . Some notes on the van der Waerden conjecture . Linear Algebra and Appl. , 4 ( 45 ) : 155 – 160 .
  • Marcus , Marvin and Newman , Morris . 1959 . On the minimum of the permanent of a doubly stochastic matrix . Duke Math. J. , 26 ( 45 ) : 61 – 72 .
  • Minc , Henryk . 1975 . Doubly stochastic matrices with minimal permanents . Pacific J. Math. , 58 ( 45 ) : 155 – 157 .
  • Mine , Henryk . 1978 . “ Permanents, encyclopedia of mathematics and its applications ” . Vol. 6 , Reading : Addison-Wesley .
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  • Mine , Henryk . 1983 . “ The van der Waerden conjecture ” . In General Inequalities , Vol. 3 , 23 – 40 . Basel : Birkhäuser .
  • Sinkhorn , Richard and Knopp , Paul . 1969 . Problems involving diagonal products in nonnegative matrices . Trans. Amer. Math. Soc. , 136 : 67 – 75 .

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