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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 $a_{1}, a_{2}, \dots, a_{r}$ in $S$ with repetitions allowed such that $\sum_{i = 1}^{r} a_{i} = n$ . 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 $D P (n; S)$ .

We offer some relations and congruences for two interesting spt-type functions, which together form a relation to Andrews' spt function.

Currently displaying 21 – 40 of 190

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Displaying 21 – 40 of 190

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

An asymptotic formula in the theory of compositions.

An Asymptotic Formula in the Theory of Compositions. (Short Communication).

An extension of Franklin's bijection.

An infinite family of overpartition congruence modulo 12.

Analysis of an algorithm to construct Fibonacci partitions

Another smallest part function related to Andrews' spt function

Anzahl der Zerlegungen einer ganzen, rationalen Zahl in Summanden, II.

Anzahl der Zerlegungen einer ganzen rationalen Zahl in Summanden

Applications de la dérivation d'Arbogast à la solution de la partition des nombres et à d'autres problèmes

Arithmetic properties for hyper $m$ -ary partition functions.

Arithmetical consequences of two identities of B. Gordon.

Arithmetical properties of finite rings and algebras, and analytic number theory.

Arithmetical properties of finite rings and algebras, and analytic number theory. II.

Asymptotic analysis of Ramanujan pairs.

Asymptotic analysis of Ramanujan pairs. (Short Communication).

Asymptotic Formula for Distinct Partitions of Lattice Points with Congruence Restrictions.

BG-ranks and 2-cores.

Bounds for the eventual positivity of difference functions of partitions into prime powers.

Bounds on the number of integer valued monotone functions of k integer arguments

Currently displaying 21 – 40 of 190