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Numerical
semigroup tree of multiplicities 4 and 5
Abby Greco, Jesse Lansford and Michael Steward
Vol. 13 (2020), No. 2, 301–322
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Abstract |
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A numerical semigroup is a cofinite submonoid of the nonnegative integers under addition. The cardinality of the complement of in the nonnegative integers is called the genus. The smallest nonzero element of is the multiplicity of . 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. |
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Keywords
numerical semigroup, tree of numerical semigroups
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Mathematical Subject Classification 2010
Primary: 05A15, 20M14
Secondary: 11D07
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Milestones
Received: 6 August 2019
Revised: 16 December 2019
Accepted: 15 January 2020
Published: 30 March 2020
Communicated by Vadim Ponomarenko
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Authors |
| Abby Greco | |
| Department of Mathematical
Sciences United States Military Academy at West Point West Point, NY United States |
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| Jesse Lansford | |
| Department of Mathematical
Sciences United States Military Academy at West Point West Point, NY United States |
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| Michael Steward | |
| Department of Mathematical
Sciences United States Military Academy at West Point West Point, NY United States |
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