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The Frobenius
number of a family of numerical semigroups with embedding
dimension 5
Kurt Herzinger, Emelia McLaughlin and Julie Trimber |
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Vol. 16 (2023), No. 5, 833–847
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Abstract |
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We answer the Frobenius problem for a specific family of numerical semigroups with embedding dimension 5. The numerical semigroups in this family are called fulcrum numerical semigroups and are related to balanced and unitary numerical semigroups introduced in earlier research. We show that fulcrum numerical semigroups come in two distinct varieties and provide formulas for the Frobenius number and genus for both. |
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Keywords
numerical semigroup, Frobenius number, Apéry set, genus
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Mathematical Subject Classification
Primary: 20M14
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Milestones
Received: 6 June 2022
Revised: 23 December 2022
Accepted: 23 December 2022
Published: 9 December 2023
Communicated by Nathan Kaplan
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Authors |
| Kurt Herzinger | |
| Department of Mathematical
Sciences U.S. Air Force Academy Air Force Academy, CO United States |
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| Emelia McLaughlin | |
| Department of Mathematical
Sciences U.S. Air Force Academy Air Force Academy, CO United States |
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| Julie Trimber | |
| Department of Mathematical
Sciences U.S. Air Force Academy Air Force Academy, CO United States |
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| © 2023 This work is in the public domain. |
