The first elements of the quotient of a numerical semigroup by a positive integer

Abstract

Given three pairwise coprime positive integers $a_1,a_2,a_3\in {\mathbb{Z}}^{+}$ we show the existence of a relation between the sets of the first elements of the three quotients $\frac{⟨a_i,a_j⟩}{a_k}$ that can be made for every $\{i.j,k\}=\{1,2,3\}$. Then we use this result to give an improved version of Johnson's semi-explicit formula for the Frobenius number $g(a_1,a_2,a_3)$ without restriction on the choice of $a_1,a_2,a_3$ and to give an explicit formula for a particular class of numerical semigroups.

arXiv comment7 pages

Cited by in corpus (1)

• On the genus of a quotient of a numerical semigroup