文献类型：期刊文献

英文题名：An extension of Pólya's enumeration theorem

作者：Zhan, Xiongfeng[1];Huang, Xueyi[1]

机构：[1]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China

年份：2025

卷号：348

期号：6

外文期刊名：DISCRETE MATHEMATICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001428675800001)】；

基金：The authors are grateful to Professor T. Amdeberhan for his insightful comments and to the anonymous referees for their constructive suggestions. X. Huang was supported by National Natural Science Foundation of China (Grant No. 12471324) and Natural Science Foundation of Shanghai (Grant No. 24ZR1415500) .

语种：英文

外文关键词：P & oacute;lya's enumeration theorem; Cycle index polynomial; Determinant

摘要：In combinatorics, P & oacute;lya'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 P & oacute;lya's Enumeration Theorem. As an application, we derive a formula that expresses the n-th elementary symmetric polynomial in m indeterminates (where n <= m) as a variant of the cycle index polynomial of the symmetric group Sym(n). This result resolves a problem posed by Amdeberhan in 2012. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.