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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.12508 |
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Table of Contents:
- In combinatorics, Pólya's Enumeration Theorem is a powerful tool for solving a wide range of counting problems, including the enumeration of groups, graphs, and chemical compounds. In this paper, we present an extension of Pólya's Enumeration Theorem. As an application, we derive a formula that expresses the $n$-th elementary symmetric polynomial in $m$ indeterminates (where $n\leq m$) as a variant of the cycle index polynomial of the symmetric group $\mathrm{Sym}(n)$. This result resolves a problem posed by Amdeberhan in 2012.