On k-sparse numerical semigroups
G. Tizziotti, J. Villanueva
TL;DR
This paper introduces and studies k-sparse numerical semigroups, a generalization of sparse semigroups, focusing on the spacing between non gaps below the conductor.
Contribution
It defines the class of k-sparse numerical semigroups and explores their properties, extending the concept of sparse semigroups.
Findings
Characterization of k-sparse semigroups
Generalization of sparse semigroups
Structural properties of k-sparse semigroups
Abstract
Given a positive integer k, we investigate the class of numerical semigroups verifying the property that every two subsequent non gaps, smaller than the conductor, are spaced by at least k. These semigroups will be called k-sparse and generalize the concept of sparse numerical semigroups.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic Geometry and Number Theory · Polynomial and algebraic computation