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arXiv · 1807.10907

The number of addends in the decomposition of an element of a numerical semigroup into atoms

Hamid Kulosman
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Abstract

We prove that for every nonempty set $\Sigma$ of integers bigger than $1$, which has at most three elements, there exists a numerical semigroup $T$ and an element $x$ of $T$ such that a natural number $n$ is the number of atoms in a decomposition of $x$ into atoms if and only if $n$ belongs to $\Sigma$. We also propose three related conjectures.

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Hamid Kulosman. 2018-07-28. The number of addends in the decomposition of an element of a numerical semigroup into atoms. https://arxiv.org/abs/1807.10907

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