@article{Chen2025, 
author = {Marta Na Chen and Wenchang Chu},
title = {Multiple sums for cyclically symmetric products of binomial coefficients},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {12},
pages = {29236-29262},
keywords = {circular sum, generating function, binomial coefficient, Lucas number, Fibonacci number, Lagrange expansion formula},
url = {https://www.sciopen.com/article/10.3934/math.20251285},
doi = {10.3934/math.20251285},
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.}
}