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arXiv · 1908.06448

Elasticity in Apery sets

Jackson Autry·Tara Gomes·Christopher O'Neill·Vadim Ponomarenko
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Abstract

A numerical semigroup $S$ is an additive subsemigroup of the non-negative integers, containing zero, with finite complement. Its multiplicity $m$ is its smallest nonzero element. The Apery set of $S$ is the set $\text{Ap}(S) = \{n \in S : n-m \notin S\}$. Fixing a numerical semigroup, we ask how many elements of its Apery set have nonunique factorization, and define several new invariants.

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Jackson Autry, Tara Gomes, Christopher O'Neill, Vadim Ponomarenko. 2019-08-18. Elasticity in Apery sets. https://arxiv.org/abs/1908.06448

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