Operator theorems on $L^P$-convergence to zero $(1 \leqslant p &lt; + \infty )$

R. Zaharopol

Displaying similar documents to “Operator theorems on $L^{P}$ -convergence to zero $(1 ⩽ p < + \infty)$ ”

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Ben Saïd, J.-N. Nicolas (2003)

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W. Klonecki (1966)

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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

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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 $D P (n; S)$ .