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Research Article | Open Access

Multiple sums for cyclically symmetric products of binomial coefficients

School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, China; chennamarta@zknu.edu.cn
Via Dalmazio Birago 9/E, Lecce 73100, Italy
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Abstract

Carlitz' multiple sums involving cyclically symmetric products of binomial coefficients are extended by introducing weight monomials of m-variables. By making use of recursive reductions and the Lagrange expansion formula, we determine, in closed form, the related rational generating functions that significantly generalize the classical result discovered by Carlitz in 1965. Several novel applications are presented as consequences.

Keywords

circular sumgenerating functionbinomial coefficientLucas numberFibonacci numberLagrange expansion formula
CLC number: Primary 11B39, Secondary 05A15, 11B65

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AIMS Mathematics
Volume 10 Issue 12,
December 2025
Pages 29236-29262
DOI: 10.3934/math.20251285

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Cite this article:
Chen MN, Chu W. Multiple sums for cyclically symmetric products of binomial coefficients. AIMS Mathematics, 2025, 10(12): 29236-29262. https://doi.org/10.3934/math.20251285

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Received: 17 September 2025
Revised: 27 November 2025
Accepted: 08 December 2025
Published: 12 December 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)