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The van der Waerden conjecture: Two proofs in one year. (English) Zbl 0503.15009


MSC:

15B51 Stochastic matrices
15A15 Determinants, permanents, traces, other special matrix functions
15-03 History of linear algebra
05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
01A65 Development of contemporary mathematics
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[1] Alexandroff, A. D., Zur Theorie der gemischten Volumina von konvexen Körpern IV, Mat. Sbornik, 3, 45, 227-251 (1938) · JFM 64.1347.01
[2] Egoritsjev, G. P., Solution of van der Waerden’s permanent conjecture, preprint 13M of the Kirenski Institute of Physics, Krasnojarsk (1980), (Russian) translation in: Advances in Math., 42, 299-305 (1981) · Zbl 0478.15003
[3] Falikman, D. I., A proof of the van der Waerden conjecture on the permanent of a doubly stochastic matrix, Matematičeski Zametki, 29, 931-938 (1981) · Zbl 0475.15007
[4] Fenchel, Werner, Inégalités quadratiques entre les volumes mixtes des corps convexes. Comptes Rendus, Acad. Sci, Paris, 203, 647-650 (1936) · Zbl 0015.12006
[5] Knuth, D. E., A permanent inequality (to appear in Am. Math, Monthly, 88, 731-740 (1981) · Zbl 0478.15004 · doi:10.2307/2321472
[6] van Lint, J. H., Notes on Egoritsjev’s Proof of the van der Waerden Conjecture, Linear Algebra and its Applications, 39, 1-8 (1981) · Zbl 0468.15005 · doi:10.1016/0024-3795(81)90285-8
[7] London, D., Some notes on the van der Waerden Conjecture, Linear Algebra and its Applications, 4, 155-160 (1971) · Zbl 0262.15007 · doi:10.1016/0024-3795(71)90036-X
[8] Marcus, Marvin; Newman, Morris, On the minimum of the permanent of a doubly stochastic matrix, Duke Math J., 26, 61-72 (1959) · Zbl 0168.28002 · doi:10.1215/S0012-7094-59-02606-7
[9] Mine, H., Permanents, Encyclopedia of Mathematics and its Applications, vol. 6 (1978), Reading, Mass: Addison-Wesley, Reading, Mass · Zbl 0401.15005
[10] Stanley, R. P., Two combinatorial applications of the Alekxandrov-Fenchel inequalities, J. Combinatorial Theory, 31, 56-65 (1981) · Zbl 0484.05012 · doi:10.1016/0097-3165(81)90053-4
[11] van der Waerden, B. L., Aufgabe 45, Jahresber. d. D.M.V., 35, 117-117 (1926)
[12] van der Waerden, B. L., Ein Satz iiber Klasseneinteilungen von endlichen Mengen, Abh. a. d. Math. Seminar Hamburg, 5, 185-188 (1927) · JFM 53.0171.02 · doi:10.1007/BF02952519
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