# Symmetric, pseudo-symmetric, and almost-symmetric numerical semigroups

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A numerical semigroup $S$ is a submonoid of $(\mathbb N,+)$ with finite complement in $\mathbb N$. Integers not in $S$ are called gaps of $S$. The largest gap is known as the Frobenius number of $S$, $F(S)$. A gap $x$ is a hole, if $F(S)-x$ is also a gap.

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