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Title: Numerical Semigroups, Polyhedra, and Posets III: Minimal Presentations and Face Dimension
This paper is the third in a series of manuscripts that examine the combinatorics of the Kunz polyhedron $$P_m$$, whose positive integer points are in bijection with numerical semigroups (cofinite subsemigroups of $$\mathbb Z_{\ge 0}$$) whose smallest positive element is $$m$$. The faces of $$P_m$$ are indexed by a family of finite posets (called Kunz posets) obtained from the divisibility posets of the numerical semigroups lying on a given face. In this paper, we characterize to what extent the minimal presentation of a numerical semigroup can be recovered from its Kunz poset. In doing so, we prove that all numerical semigroups lying on the interior of a given face of $$P_m$$ have identical minimal presentation cardinality, and we provide a combinatorial method of obtaining the dimension of a face from its corresponding Kunz poset.  more » « less
Award ID(s):
1745638
PAR ID:
10527738
Author(s) / Creator(s):
; ;
Publisher / Repository:
The Electronic Journal of Combinatorics
Date Published:
Journal Name:
The Electronic Journal of Combinatorics
Volume:
30
Issue:
2
ISSN:
1077-8926
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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