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Title: Bracelet monoids and numerical semigroups
Authors: Rosales, J.C.
Branco, M.B.
Torrão, D.
Keywords: (n1, . . . , n p)-bracelet · Monoid · Numerical semigroup · Frobenius number · Tree
Issue Date: 2-Oct-2015
Publisher: Springer
Citation: Applicable Algebra in Engineering, Communication and Computing, pp 1-15.
Abstract: Given positive integers n1, . . . , n p, we say that a submonoid M of (N,+) is a (n1, . . . , n p)-bracelet if a +b+ n1, . . . , n p ⊆ M for every a, b ∈ M\ {0}. In this note, we explicitly describe the smallest n1, . . . , n p -bracelet that contains a finite subset X of N. We also present a recursive method that enables us to construct the whole set B(n1, . . . , n p) = M|M is a (n1, . . . , n p)-bracelet . Finally, we study (n1, . . . , n p)-bracelets that cannot be expressed as the intersection of (n1, . . . , n p)- bracelets properly containing it.
ISSN: ISSN: 0938-1279
Type: article
Appears in Collections:CIMA - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica

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