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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.
Keywords
numerical semigroup, tree of numerical semigroups
Mathematical Subject Classification 2010
Primary: 05A15, 20M14
Secondary: 11D07
Milestones
Received: 6 August 2019
Revised: 16 December 2019
Accepted: 15 January 2020
Published: 30 March 2020
Communicated by Vadim Ponomarenko