Arithmetic Terms for Multinomial Coefficient Sums
General Mathematics
2025-05-23 v12
Abstract
We construct arithmetic terms representing the partial sums of binomial coefficients, and we extend these results to obtain arithmetic terms representing the multisections of binomial coefficient sums. We also introduce an arithmetic term representing a certain type of multinomial coefficient sum and, as an application, we provide an arithmetic term representing the central trinomial coefficients. This solves one of the research problems of the celebrated book Concrete Mathematics, which remained open for nearly thirty years.
Keywords
Cite
@article{arxiv.2312.00301,
title = {Arithmetic Terms for Multinomial Coefficient Sums},
author = {Joseph M. Shunia and Lorenzo Sauras-Altuzarra},
journal= {arXiv preprint arXiv:2312.00301},
year = {2025}
}
Comments
Major revision. Title updated to reflect new content. Includes new proofs and refinements. Lorenzo Sauras-Altuzarra has joined as a coauthor in recognition of his substantial contributions