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arXiv · 1701.08555

Minimal presentations of shifted numerical monoids

Rebecca Conaway·Felix Gotti·Jesse Horton·Christopher O'Neill·Roberto Pelayo·Mesa Williams·Brian Wissman
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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 examine minimal relations among the generators of $M_n$ when $n$ is sufficiently large, culminating in a description that is periodic in the shift parameter $n$. We explore several applications to computation, combinatorial commutative algebra, and factorization theory.

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Rebecca Conaway, Felix Gotti, Jesse Horton, Christopher O'Neill, Roberto Pelayo, Mesa Williams, Brian Wissman. 2017-01-30. Minimal presentations of shifted numerical monoids. https://doi.org/10.1142/s0218196718500030

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