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Restricted Partitions of Finite Sets

Published online by Cambridge University Press:  20 November 2018

F.L. Miksa ,
L. Moser  and
M. Wyman
M. Wyman
Affiliation:
University of Alberta
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In this paper we consider the following combinatorial problem. In how many ways can n distinguishable objects be placed into an unrestricted number of indistinguishable boxes, if each box can hold at most r objects? Let us denote this number by Gn, r

Special cases of this problem have been the object of considerable study. In the case r = 2 we have the numbers Gn, 2 = Tn which have been treated by Rothe [12] as early as 1800. Tn is also the number of solutions of x2 = 1 in the symmetric group on n letters , and in this and related guises has been studied by Touchard [13], Chowla, Herstein and Moore [3] and two of the present authors [7].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 1 , Issue 2 , May 1958 , pp. 87 - 96
Copyright
Copyright © Canadian Mathematical Society 1958

References

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