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arXiv · 1708.09527

Ap\'ery sets of shifted numerical monoids

Christopher O'Neill·Roberto Pelayo
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Abstract

A numerical monoid is an additive submonoid of the non-negative integers. Given a numerical monoid $S$, consider the family of "shifted" monoids $M_n$ obtained by adding $n$ to each generator of $S$. In this paper, we characterize the Ap\'ery set of $M_n$ in terms of the Ap\'ery set of the base monoid $S$ when $n$ is sufficiently large. We give a highly efficient algorithm for computing the Ap\'ery set of $M_n$ in this case, and prove that several numerical monoid invariants, such as the genus and Frobenius number, are eventually quasipolynomial as a function of $n$.

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Christopher O'Neill, Roberto Pelayo. 2017-08-31. Ap\'ery sets of shifted numerical monoids. https://doi.org/10.1016/j.aam.2018.01.005

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