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arXiv · 1912.04460

Numerical semigroups, polyhedra, and posets II: locating certain families of semigroups

Jackson Autry·Abigail Ezell·Tara Gomes·Christopher O'Neill·Christopher Preuss·Tarang Saluja·Eduardo Torres Davila
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Abstract

Several recent papers have examined a rational polyhedron $P_m$ whose integer points are in bijection with the numerical semigroups (cofinite, additively closed subsets of the non-negative integers) containing $m$. A combinatorial description of the faces of $P_m$ was recently introduced, one that can be obtained from the divisibility posets of the numerical semigroups a given face contains. In this paper, we study the faces of $P_m$ containing arithmetical numerical semigroups and those containing certain glued numerical semigroups, as an initial step towards better understanding the full face structure of $P_m$. In most cases, such faces only contain semigroups from these families, yielding a tight connection to the geometry of $P_m$.

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Jackson Autry, Abigail Ezell, Tara Gomes, Christopher O'Neill, Christopher Preuss, Tarang Saluja, Eduardo Torres Davila. 2019-12-10. Numerical semigroups, polyhedra, and posets II: locating certain families of semigroups. https://arxiv.org/abs/1912.04460

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