# Enumeration of Numerical Semigroups {0}∪[a,b]∪[c,∞) with Same Embedding Dimension

## Abstract

We consider the set $S$ defined as $\{0\}\cup[a,b]\cup[c,\infty)$ where $[a,b]$ be the set of all integer $x$ such that $a\leq&space;x&space;\leq&space;b$ and $[c,\infty)$ be the set integer $y$ such that $c\leq&space;y$ when $a,b$ and $c$ are positive integers satisfying $2&space;\leq&space;a\leq&space;b&space;$. It is known that $S$ is a numerical semigroup if and only if $c\leq&space;2a$. This research aims to characterize the minimal system of generators for numerical semigroups $S$ and determine the count of numerical semigroups $\{0\}\cup[a,b]\cup[c,\infty)$ that share the same embedding dimension.

Section
บทความวิจัย

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