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On the Problème Des Ménages

Published online by Cambridge University Press:  20 November 2018

Max Wyman  and
Leo Moser
Max Wyman
Affiliation:
University of Alberta
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The classical problème des ménages asks for the number of ways of seating at a circular table n married couples, husbands and wives alternating, so that no husband is next to his own wife.

An outline of the history of the problem to 1946 was given by Kaplansky and Riordan (11). They also presented a bibliography, which is augmented and brought up to date in the bibliography of the present paper.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 468 - 480
Copyright
Copyright © Canadian Mathematical Society 1958

References

1. Ahrens, W., Mathematische Unterhaltungen und Spiele, vol. 2 (2-aufl., Leipzig, 1918), 73-79.Google Scholar
2. Carlitz, L., Congruences for the ménage polynomials, Duke Math. J., 19 (1952), 549-552.Google Scholar
3. Carlitz, L., Congruence properties of the ménage polynomials, Scripta Math., 20 (1954), 51-57.Google Scholar
4. Cayley, A., A problem on arrangements, Proc. Roy. Soc. Edin., 9 (1878), 338-342.Google Scholar
5. Cayley, A., Note on Mr. Muir's solution of a problem of arrangements, Proc. Roy. Soc. Edin. 9 (1878), 388-391.Google Scholar
6. Dorrie, H., Triumph der Mathematik (2 aufl., Breslau, 1940), 25-32.Google Scholar
7. Erdös, P. and Kaplansky, I., The asymptotic number of Latin rectangles, Amer. J. Math., 68 (1946), 230-236.Google Scholar
8. Joseph, A. W., A problem in derangements, J. Inst. Actuaries Students Soc. (1946), 14-22.Google Scholar
9. Kaplansky, I., Solution of the “Problème des ménages,” Bull. Amer. Math. Soc, 49 (1943), 784-785.Google Scholar
10. Kaplansky, I., Symbolic solution of certain problems in permutations, Bull. Amer. Math. Soc, 50 (1944), 906-914.Google Scholar
11. Kaplansky, I. and Riordan, J., The problème des ménages. Scripta Math., 12 (1946), 113-124.Google Scholar
12. Kerawala, S. M., Asymptotic solution of the problème des ménages, Bull. Calcutta Math. Soc, 39 (1947), 82-84.Google Scholar
13. Lucas, E., Théorie des Nombres (Paris, 1891), 491-495.Google Scholar
14. MacMahon, P. A., Combinatory Analysis, vol. 1 (Cambridge, 1915), 253-254.Google Scholar
15. Mendelsohn, N. S., Symbolic solution of card matching problems, Bull. Amer. Math. Soc, 50 (1946), 918-924.Google Scholar
16. Mendelsohn, N. S., The asymptotic series for a certain class of permutation problems, Can. J. Math., 8 (1956), 234-245.Google Scholar
17. Muir, T., On Professor Tait's problem of arrangements, Proc Roy. Soc Edin., 9 (1878), 382–387.Google Scholar
18. Muir, T., Additional note on a problem of arrangement, Proc. Roy. Soc Edin., 11 (1882). 187-190.Google Scholar
19. Netto, E., Lehrbuchder Combinatorik (2nd ed., Berlin, 1927), 75-80.Google Scholar
20. Riordan, J.,The arithmetic of the ménage numbers, Duke Math. J., 19 (1952), 27-30.Google Scholar
21. Schöbe, W., Das Lucassche Ehepaarproblem, Math. Z., 48 (1943), 781-784.Google Scholar
22. Tait, P. G., Scientific Papers, vol. 1 (Cambridge, 1898), 287.Google Scholar
23. Touchard, J., Sur un problème de permutations, C. R. 198 (Paris, 1934), 631-633.Google Scholar
24. Touchard, J., Permutations discordant with two given permutations, Scripta Math. 19 (1953), 109-119.Google Scholar
25. Yamamoto, K., On the asymptotic number of Latin rectangles, Jap. J. Math., 21 (1952), 113-119.Google Scholar
26. Yamamoto, K., An asymptotic series for the number of three-line Latin rectangles, J. Math. Soc Japan, 1 (1950), 226-221.Google Scholar