Year: 2023
Type: preprint
Abstract: If $S$ is a numerical semigroup, let $m(S,k)$ denote the number of ideals of $S$ with codimension $k$ and let $n(S,k)$ denote the number of ideals of $S$ with conductor $k$. We compute the generating function of the sequence $m(S,k)$ for all numerical semigroups of embedding dimension $2$ and for $S = \langle 3,n+2,2n+1\rangle$. We also prove that the sequence $n(S,k)$ becomes stationary after a certain term and compute the stationary terms for numerical semigroups of the form $\langle a,a+1 \rangle$.
Source: arXiv (Cornell University)
Author: Chavan, Parth
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4367190966