On the Numerical Semigroup Generated by 2k−m⋅2n+i−1|i∈ℕ

Abstract

Let k,n be two positive integers such that 2≤k≤2n and m be an odd number with 1≤m<2k−1. Denote by Tk,m,n a numerical semigroup generated by 2k−m⋅2n+i−1|i∈ℕ. In this paper, we give the formula for the embedding dimension of Tk,m,n. In particular, the formulas for computing the Frobenius number and the genus of Tk,2t+1,n with 2≤t<k−1 are given.