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

Title:

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

Creator:

Xiaojun, Wu and Chao, Chong-Yun

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:39c7d190-c22b-4f04-a20f-0fa25cf0fe73
uuid:39c7d190-c22b-4f04-a20f-0fa25cf0fe73

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

Type:

model:article and TEXT

Format:

bez média and svazek

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 ${\mathrm DP}(n;S)$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

611-623

Source:

Czechoslovak Mathematical Journal | 2005 Volume:55 | Number:3

Harvested from:

CDK

Metadata only:

false