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An application of Pólya’s enumeration theorem to partitions of subsets of positive integers

Xiao Jun Wu, Chong-Yun Chao (2005)

Czechoslovak Mathematical Journal

Let S be a non-empty subset of positive integers. A partition of a positive integer n into S is a finite nondecreasing sequence of positive integers a 1 , a 2 , , a r in S with repetitions allowed such that i = 1 r a i = n . Here we apply Pólya’s enumeration theorem to find the number ( n ; S ) of partitions of n into S , and the number D P ( n ; S ) of distinct partitions of n into S . We also present recursive formulas for computing ( n ; S ) and D P ( n ; S ) .

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