On Leonid Gurvits's proof for permanents

American Mathematical Monthly

Volumn 117, Issue 10, 2010, Pages 903-911

  Laurent, Monique ^a,b   Schrijver, Alexander ^a,c  

^a CWI   (Netherlands)

^b TILBURG UNIVERSITY   (Netherlands)

^c UNIVERSITY OF AMSTERDAM   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78651070765     PISSN: 00029890     EISSN: None     Source Type: Journal    
DOI: 10.4169/000298910X523380     Document Type: Article

References (20)

1. T. Bang, On Matrix-Functions Giving a Good Approximation to the v.d. Waerden Permanent Conjecture, Preprint Series 1979 No. 30, Matematisk Institut, Københavns Universitet, Copenhagen, 1979.
2. A.-L. Cauchy, Mémoire sur les fonctions qui ne peuvent obtenir que deux valeurs égales et de signes contraires par suite des transpositions opérées entre les variables qu'elles renferment, Journal de l'École Polytechnique 27(10) (1812) 29-112.
3. M. Ciucu, An improved upper bound for the 3-dimensional dimer problem, Duke Math. J. 94 (1998) 1-11.doi: 10.1215/S0012-7094-98-09401-7
4. G. P. Egorychev, Proof of the van der Waerden conjecture for permanents (in Russian), Sibirsk. Mat. Zh. 22(6) (1981) 65-71;
5. English translation, Siberian Math. J. 22 (1981) 854-859. doi:10.1007/ BF00968054
6. P. Erdõs and A. Rényi, On random matrices II, Studia Sci. Math. Hungar. 3 (1968) 459-464.
7. D. I. Falikman, Proof of the van der Waerden conjecture regarding the permanent of a doubly stochastic matrix (in Russian), Mat. Zametki 29 (1981) 931-938;
8. English translation, Math. Notes 29 (1981) 475-479.
9. S. Friedland, A lower bound for the permanent of a doubly stochastic matrix, Ann. of Math. (2) 110 (1979) 167-176. doi:10.2307/1971250
10. L. Gurvits, Van der Waerden/Schrijver-Valiant like conjectures and stable (aka hyperbolic) homogeneous polynomials: One theorem for all, Electron. J. Combin. 15 (2008) R66.
11. D. E. Knuth, A permanent inequality, Amer. Math. Monthly 88 (1981) 731-740. doi : 10.2307/2321472
12. J. H. van Lint, Notes on Egoritsjev's proof of the van der Waerden conjecture, Linear Algebra Appl. 39 (1981)1-8. doi:10.1016/0024-3795(81)90285-8
13. -, The van der Waerden conjecture: Two proofs in one year, Math. Intelligencer 4(2) ( 1982) 72-77. doi: 10.1007/BF03023485
14. H. Mine, Permanents, Addison-Wesley, Reading, MA, 1978.
15. A. Schrijver, Counting 1-factors in regular bipartite graphs, J. Combin. Theory Ser. B 72 (1998) 122-135. doi: 10.1006/jctb.1997.1798
16. A. Schrijver and W G. Valiant, On lower bounds for permanents, Indag. Math. (N.S.) 42 (1980) 425-427.
17. M. Voorhoeve, A lower bound for the permanents of certain (0, 1)-matrices, Indag. Math. (N.S.) 41 (1979) 83-86.
18. B. L. van der Waerden, [Aufgabe] 45, Jahresber. Deutsch. Math.-Verein. 35 (1926) 117.
19. I. M. Wanless, Addendum to Schrijver's work on minimum permanents, Combinatorica 26 (2006) 743-745. doi:10.1007/s00493-006-0040-z
20. H. S. Wilf, On the permanent of a doubly stochastic matrix, Canad. J. Math. 18 (1966) 758-761.