The Frobenius problem for Numerical Semigroups generated by binomial coefficients
Number Theory
2025-10-06 v3
Abstract
The greatest integer that does not belong to a numerical semigroup is called the Frobenius number of , and finding the Frobenius number is called the Frobenius problem. In this paper, we solve the Frobenius problem for the numerical semigroups generated by binomial coefficients. As applications, we provide some nontrivial identities among binomial coefficients, and we also connect the main results to the theory of -core partitions of integers.
Keywords
Cite
@article{arxiv.2412.17882,
title = {The Frobenius problem for Numerical Semigroups generated by binomial coefficients},
author = {WonTae Hwang and Kyunghwan Song},
journal= {arXiv preprint arXiv:2412.17882},
year = {2025}
}
Comments
16 pages. arXiv admin note: substantial text overlap with arXiv:1706.09246