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A Note on the van Der Waerden Permanent Conjecture

Published online by Cambridge University Press:  20 November 2018

Jacques Dubois
Jacques Dubois*
Affiliation:
Université de Sherbrooke, Sherbrooke, Québec
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The permanent of an n-square complex matrix P = (pij) is defined by

where the summation extends over Sn, the symmetric group of degree n. This matrix function has considerable significance in certain combinatorial problems [6; 7]. The properties and many related problems about the permanent are presented in [3] along with an extensive bibliography.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 2 , April 1974 , pp. 352 - 354
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Eberlein, P. J. and Mudholkar, G. S., Some remarks on the van der Waerden Conjecture, J. Combinatorial Theory 5 (1968), 386–396.Google Scholar
2. Eberlein, P. J., Remarks on the van der Waerden Conjecture, II, Linear Algebra and Appl. 2 (1969), 311–320.Google Scholar
3. Marcus, Marvin and Minc, Henryk, Permanents, Amer. Math. Monthly 72 (1965), 577–591.Google Scholar
4. Marcus, Marvin and Newman, Morris, On the minimum of the permanent of a doubly stochastic matrix, Duke Math. J. 26 (1959), 61–72.Google Scholar
5. Ryser, H. J., Combinatorial mathematics (Carus Math. Monograph no. 14, 1963).Google Scholar
6. Ryser, H. J., Permanents and systems of distinct representatives (with discussion), Combinatorial Mathematics and its Applications (Proc. Conf., Univ. North Carolina, Chapel Hill, N.C., 1967) pp. 55-70. Univ. North Carolina Press, Chapel Hill, N.C., 1969.Google Scholar
7. van der Waerden, B. L., Aufgabe 45, Jber. Deutsch. Math.-Verein. 35 (1926), 117.Google Scholar