The Frobenius problem for Numerical Semigroups generated by binomial coefficients

2024/12/23 by Hwang, WonTae, Song, Kyunghwan
#05A10 #05A17 #11A07 #11B65 #FOS: Mathematics #Number Theory (math.NT) #Primary 11A67

paper · doi:10.48550/arxiv.2412.17882

Abstract

The greatest integer that does not belong to a numerical semigroup S is called the Frobenius number of S, 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)-core partitions of integers.

Related

• The Frobenius problem for four numerical semigroups
• The Frobenius problem for Generalized Thabit numerical semigroups
• p-numerical semigroups with p-symmetric properties
• A Note on Generalized Repunit Numerical Semigroups
• The Frobenius problem for numerical semigroups generated by sequences\n that satisfy a linear recurrence relation