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An Application of Polya's Enumeration Theorem to Partitions of Subsets of Positive Integers

Authors:	Xiaojun Wu Chong-Yun Chao

Institution:	(1) Department of Mathematics, University of Pittsburgh, PA, 15260, U.S.A.

Abstract:	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 $\sum\limits_{i = 1}^r {a_i = n}$ . Here we apply Polya's enumeration theorem to find the number P(n; S) of partitions of n into S, and the number DP(n; S) of distinct partitions of n into S. We also present recursive formulas for computing P(n; S) and DP(n; S).

Keywords:	Polya's enumeration theorem partitions of a positive integer into a non-empty subset of positive integers distinct partitions of a positive integer into a non-empty subset of positive integers recursive formulas and algorithms
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