Publicado
Numerical monoids with concentration two
Monoides numéricos de concentración dos
DOI:
https://doi.org/10.15446/bol.mat.v33n1.125712Palabras clave:
Monoides númericos de concentración 2, monoides númericos compactos, número de Frobenius y género (es)Numerical semigroups, Packed numerical monoids, Frobenius number and genus (en)
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En este artículo estudiamos el conjunto MN(m, 2) de monoides numéricos con multiplicidad m y concentración 2. Damos una partición de MN(m, 2) indexada por el conjunto PMN(m, 2) de monoides comprimidos con multiplicidad m y concentración 2. Luego construimos una aplicación biyectiva entre PMN(m, 2) y D(m) = {X ⊆{m + 1, . . . , 2m−1}|X ̸= ∅y X no contiene enteros consecutivos}. Como consecuencia, obtenemos un algoritmo para calcular todos los elementos de MN(m, 2). También clasificamos los elementos de MN(m, 2) con minima dimensión de inmersión y resolvemos el problema de Frobenius para esta clase de semigrupos.
In this paper, we study the set MN(m, 2) of numerical monoids with multiplicity m and concentration 2. We provide a partition of MN(m, 2) indexed by the set PMN(m, 2) of packed monoids with multiplicity m and concentration 2. We then construct a bijective map between PMN(m, 2) and D(m) = {X ⊆{m + 1, . . . , 2m−1}|X ̸= ∅and X contains no consecutive integers}. As a consequence, we obtain an algorithm for computing all elements of MN(m, 2). We also classify the elements in MN(m, 2) having minimal embedding dimension and solve the Frobenius problem for this class.
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