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Semigroups with fixed multiplicity and embedding dimension

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URI: http://hdl.handle.net/10498/21965

DOI: 10.26493/1855-3974.1937.5ea

ISSN: 1855-3966

ISSN: 1855-3974

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Author/s
García García, Juan IgnacioAuthority UCA; Marín Aragón, DanielAuthority UCA; Moreno Frías, María ÁngelesAuthority UCA; Rosales, José Carlos; Vigneron Tenorio, AlbertoAuthority UCA
Date
2019
Department
Matemáticas
Source
Ars Mathematica Contemporanea 17 (2019) 397–417
Abstract
Given m is an element of N, a numerical semigroup with multiplicity m is called a packed numerical semigroup if its minimal generating set is included in {m, m + 1 , ..., 2m - 1}. In this work, packed numerical semigroups are used to build the set of numerical semigroups with a given multiplicity and embedding dimension, and to create a partition of this set. Wilf's conjecture is verified in the tree associated to some packed numerical semigroups. Furthermore, given two positive integers m and e, some algorithms for computing the minimal Frobenius number and minimal genus of the set of numerical semigroups with multiplicity m and embedding dimension e are provided. We also compute the semigroups where these minimal values are achieved.
Subjects
Embedding dimension; multiplicity; numerical semigroup; Frobenius number; genus
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