On the genus of a quotient of a numerical semigroup

Abstract

We find a relation between the genus of a quotient of a numerical semigroup $S$ and the genus of $S$ itself. We use this identity to compute the genus of a quotient of $S$ when $S$ has embedding dimension $2$. We also exhibit identities relating the Frobenius numbers and the genus of quotients of numerical semigroups that are generated by certain types of arithmetic progressions.

References in corpus (4)

• Counting Numerical Semigroups
• Numerical semigroups problem list
• Minimal genus of a multiple and Frobenius number of a quotient of a numerical semigroup
• The first elements of the quotient of a numerical semigroup by a positive integer

Cited by in corpus (2)

• Quotients of numerical semigroups generated by two numbers
• On quotients of numerical semigroups for almost arithmetic progressions