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

Wu, Xiao Jun, and Chao, Chong-Yun. "An application of Pólya’s enumeration theorem to partitions of subsets of positive integers." Czechoslovak Mathematical Journal 55.3 (2005): 611-623. <http://eudml.org/doc/30972>.

@article{Wu2005,
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 $a_1, a_2, \dots , a_r$ 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 $\{\mathrm \{D\}P\}(n;S)$ of distinct partitions of $n$ into $S$. We also present recursive formulas for computing $¶(n;S)$ and $\{\mathrm \{D\}P\}(n;S)$.},
author = {Wu, Xiao Jun, Chao, Chong-Yun},
journal = {Czechoslovak Mathematical Journal},
keywords = {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; recursive formulas and algorithms},
language = {eng},
number = {3},
pages = {611-623},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An application of Pólya’s enumeration theorem to partitions of subsets of positive integers},
url = {http://eudml.org/doc/30972},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Wu, Xiao Jun
AU - Chao, Chong-Yun
TI - An application of Pólya’s enumeration theorem to partitions of subsets of positive integers
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 3
SP - 611
EP - 623
AB - 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 ${\mathrm {D}P}(n;S)$ of distinct partitions of $n$ into $S$. We also present recursive formulas for computing $¶(n;S)$ and ${\mathrm {D}P}(n;S)$.
LA - eng
KW - 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; recursive formulas and algorithms
UR - http://eudml.org/doc/30972
ER -