Semigroups with fixed multiplicity and embedding dimension
| Autor: | D. Marín-Aragón, M. A. Moreno-Frías, Juan Ignacio García-García, José Carlos Rosales, Alberto Vigneron-Tenorio |
|---|---|
| Přispěvatelé: | Matemáticas |
| Rok vydání: | 2019 |
| Předmět: |
Embedding dimension
TheoryofComputation_COMPUTATIONBYABSTRACTDEVICES Numerical semigroups Semigrupos numéricos Theoretical Computer Science Combinatorics Numerical semigroup TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY Discrete Mathematics and Combinatorics Partition (number theory) Mathematics Algebra and Number Theory Conjecture Genus Mathematics::Operator Algebras Multiplicidad Multiplicity (mathematics) Número de Frobenius TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES Multiplicity Generating set of a group Embedding Geometry and Topology Frobenius number MathematicsofComputing_DISCRETEMATHEMATICS |
| Zdroj: | UVaDOC. Repositorio Documental de la Universidad de Valladolid Consejo Superior de Investigaciones Científicas (CSIC) Digibug. Repositorio Institucional de la Universidad de Granada instname Ars mathematica contemporanea Ars Mathematica Contemporanea 17 (2019) 397–417 RODIN. Repositorio de Objetos de Docencia e Investigación de la Universidad de Cádiz |
| Popis: | Producción Científica Given m ∈ 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 Ministerio de Economía, Industria y Competitividad (project MTM2017-84890-P) Ministerio de Economía, Industria y Competitividad - Fondo Europeo de Desarrollo Regional (project MTM2015-65764-C3-1-P) |
| Databáze: | OpenAIRE |
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