English

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 SS is called the Frobenius number of SS, 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 (s,s+1,s+p)(s,s+1,s+p)-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

R2 v1 2026-06-28T20:47:17.905Z