Analytical formulas computed the embedding dimension, Frobenius number, and genus for numerical semigroups generated by specific integer combinations.
Let k, b, n be positive integers such that b ≥ 2 and 1≤k≤bn−1b−1. Denote by S(k, b, n) the numerical semigroup generated by (bk−1)⋅bn+i+1+bn+i−1b−1i∈N. In this paper, we give formulas for computing the embedding dimension, the Frobenius number, and the genus of S(k, b, n).
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Gu et al. (2026) studied this question.
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