Geodesic
Restricted Partitions of Finite Sets
Canadian mathematical bulletin, Tome 1 (1958) no. 2, pp. 87-96

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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, rSpecial 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]. 
Wyman, M. Restricted Partitions of Finite Sets. Canadian mathematical bulletin, Tome 1 (1958) no. 2, pp. 87-96. doi: 10.4153/CMB-1958-010-2
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     author = {Wyman, M.},
     title = {Restricted {Partitions} of {Finite} {Sets}},
     journal = {Canadian mathematical bulletin},
     pages = {87--96},
     year = {1958},
     volume = {1},
     number = {2},
     doi = {10.4153/CMB-1958-010-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1958-010-2/}
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