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2020 Numerical semigroup tree of multiplicities 4 and 5
Abby Greco, Jesse Lansford, Michael Steward
Involve 13(2): 301-322 (2020). DOI: 10.2140/involve.2020.13.301

Abstract

A numerical semigroup S is a cofinite submonoid of the nonnegative integers under addition. The cardinality of the complement of S in the nonnegative integers is called the genus. The smallest nonzero element of S is the multiplicity of S. There is an extensive literature about the tree of numerical semigroups, which has been used to count numerical semigroups by genus, yet the structure of the tree itself has not been described in the literature. In this paper, we completely describe the structure of the subtrees of the numerical semigroup tree of multiplicities 4 and 5. We conclude with an application of these numerical semigroup trees’ structure.

Citation

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Abby Greco. Jesse Lansford. Michael Steward. "Numerical semigroup tree of multiplicities 4 and 5." Involve 13 (2) 301 - 322, 2020. https://doi.org/10.2140/involve.2020.13.301

Information

Received: 6 August 2019; Revised: 16 December 2019; Accepted: 15 January 2020; Published: 2020
First available in Project Euclid: 25 June 2020

zbMATH: 07184486
MathSciNet: MR4080496
Digital Object Identifier: 10.2140/involve.2020.13.301

Subjects:
Primary: 05A15, 20M14
Secondary: 11D07

Rights: Copyright © 2020 Mathematical Sciences Publishers

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