Parametrizing Arf numerical semigroups
P. A. Garc\'ia-S\'anchez, B. A. Heredia, H. \.I. Karaka\c{s} and, J. C. Rosales
TL;DR
This paper develops procedures to compute and characterize Arf numerical semigroups based on parameters like genus, conductor, Frobenius number, and multiplicity, advancing understanding of their structure.
Contribution
It introduces new methods for calculating and characterizing Arf numerical semigroups with specific parameters, including their Kunz coordinates.
Findings
Procedures to compute Arf semigroups with given genus and conductor.
Characterization of Kunz coordinates for Arf semigroups.
Description of Arf semigroups with fixed Frobenius number and small multiplicity.
Abstract
We present procedures to calculate the set of Arf numerical semigroups with given genus, given conductor and given genus and conductor. We characterize the Kunz coordinates of an Arf numerical semigroup. We also describe Arf numerical semigroups with fixed Frobenius number and multiplicity up to six.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic Geometry and Number Theory · Polynomial and algebraic computation