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arXiv · 1404.2629

Position Vectors of Numerical Semigroups

Lance Bryant·James Hamblin
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Abstract

We provide a new way to represent numerical semigroups by showing that the position of every Apéry set of a numerical semigroup $S$ in the enumeration of the elements of $S$ is unique, and that $S$ can be re-constructed from this "position vector." We extend the discussion to more general objects called numerical sets, and show that there is a one-to-one correspondence between $m$-tuples of positive integers and the position vectors of numerical sets closed under addition by $m+1$. We consider the problem of determining which position vectors correspond to numerical semigroups.

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Lance Bryant, James Hamblin. 2014-07-14. Position Vectors of Numerical Semigroups. https://arxiv.org/abs/1404.2629

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