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Title: Numerical semigroups, polyhedra, and posets II: locating certain families of semigroups
Abstract Several recent papers have examined a rational polyhedronPmwhose integer points are in bijection with the numerical semigroups (cofinite, additively closed subsets of the non-negative integers) containingm. A combinatorial description of the faces ofPmwas 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 ofPmcontaining arithmetical numerical semigroups and those containing certain glued numerical semigroups, as an initial step towards better understanding the full face structure ofPm. In most cases, such faces only contain semigroups from these families, yielding a tight connection to the geometry ofPm.  more » « less
Award ID(s):
1851542
PAR ID:
10503511
Author(s) / Creator(s):
; ; ; ; ; ;
Publisher / Repository:
De Gruyter
Date Published:
Journal Name:
Advances in Geometry
Volume:
22
Issue:
1
ISSN:
1615-715X
Page Range / eLocation ID:
33 to 48
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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