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The permanent at a minimum on certain classes of doubly stochastic matrices


Author: Mark Blondeau Hedrick
Journal: Bull. Amer. Math. Soc. 80 (1974), 836-838
MSC (1970): Primary 05B20, 60J05, 15A15, 15A51
MathSciNet review: 0360636
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  • 2. P. J. Eberlein and Govind S. Mudholkar, Some remarks on the van der Waerden conjecture, J. Combinatorial Theory 5 (1968), 386–396. MR 0231835
  • 3. Mark Blondeau Hedrick, 𝑝-minors of a doubly stochastic matrix at which the permanent achieves a minimun, Linear Algebra and Appl. 10 (1975), 177–179. MR 0360637
  • 4. David London, Some notes on the van der Waerden conjecture, Linear Algebra and Appl. 4 (1971), 155–160. MR 0291185
  • 5. Marvin Marcus and Henryk Minc, On a conjecture of B. L. van der Waerden, Proc. Cambridge Philos. Soc. 63 (1967), 305–309. MR 0206028
  • 6. Marvin Marcus and Morris Newman, On the minimum of the permanent of a doubly stochastic matrix, Duke Math. J. 26 (1959), 61–72. MR 0104679
  • 7. D. W. Sasser and M. L. Slater, On the inequality ∑𝑥ᵢ𝑦ᵢ≧(1/𝑛)∑𝑥ᵢ⋅∑𝑦ᵢ and the van der Waerden permanent conjecture, J. Combinatorial Theory 3 (1967), 25–33. MR 0217099
  • 8. B. L. van der Waerden, Aufgabe 45, Jber. Deutsch. Math.-Verein. 35 (1926), 117.

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DOI: https://doi.org/10.1090/S0002-9904-1974-13532-9