Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-23T12:18:26.974Z Has data issue: false hasContentIssue false

The Asymptotic Series For a Certain Class Of Permutation Problems

Published online by Cambridge University Press:  20 November 2018

N. S. Mendelsohn*
Affiliation:
University of Manitoba
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

1. Introduction. This paper is concerned with problems connected with the permutations of the integers 1, 2, … , n subject to certain special restrictions. One such class of problems, the so-called “card matching” problems, deals with conditions of the type, “the number i is in the jth position,” “the number k is in the mth position,” etc.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Broderick, T. S., On some symbolic formulae in probability theory, Proc. Roy. Irish Acad., 44 (1937), 1928.Google Scholar
2. Fréchet, M., Les probabilités associées à un système d'événements compatibles et dependentst, Actualités Scientifiques et Industrielles, nos 859 et 942 (Paris, 1940 and 1943).Google Scholar
3. Kaplansky, I., Symbolic solution of certain problems in permutations, Bull. Amer. Math. Soc, 50 (1944), 906914.Google Scholar
4. Kaplansky, I., The asymptotic distribution of runs of consecutive elements, Ann. Math. Statist., 16 (1945), 200203.Google Scholar
5. Kaplansky, I. and Riordan, J., Le problème des ménages, Scripta Math., 12 (1946), 113124.Google Scholar
6. Kaplansky, I. and Riordan, J., The problem of the rooks and its applications, Duke Math. J., 16 (1946), 259268.Google Scholar
7. Mendelsohn, N. S., Symbolic solution of card matching problems, Bull. Amer. Math. Soc, 52 (1946), 918924.Google Scholar
8. Mendelsohn, N. S., Applications of combinational formulae to generalizations of Wilson's theorem, Can. J. Math., 1 (1949), 328336.Google Scholar
9. Riordan, J., Three line Latin rectangles II, Amer. Math. Monthly, 53 (1946), 1820.Google Scholar