1. An application of Pólya’s enumeration theorem to partitions of subsets of positive integers
- Creator:
- Xiaojun, Wu and Chao, Chong-Yun
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Pólya’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, and recursive formulas and algorithms
- Language:
- English
- Description:
- 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 $a_1, a_2, \dots , a_r$ in $S$ with repetitions allowed such that $\sum ^r_{i=1} a_i = n$. Here we apply Pólya’s enumeration theorem to find the number $¶(n;S)$ of partitions of $n$ into $S$, and the number ${\mathrm DP}(n;S)$ of distinct partitions of $n$ into $S$. We also present recursive formulas for computing $¶(n;S)$ and ${\mathrm DP}(n;S)$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public