Publisher Correction to: Distribution of genus among numerical semigroups with fixed Frobenius number
نویسندگان
چکیده
منابع مشابه
The Frobenius problem for numerical semigroups
In this paper, we characterize those numerical semigroups containing 〈n1, n2〉. From this characterization, we give formulas for the genus and the Frobenius number of a numerical semigroup. These results can be used to give a method for computing the genus and the Frobenius number of a numerical semigroup with embedding dimension three in terms of its minimal system of generators.
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Given two numerical semigroups S and T and a positive integer d, S is said to be one over d of T if S = {s ∈ N | ds ∈ T} and in this case T is called a d-fold of S. We prove that the minimal genus of the d-folds of S is g + ⌈ (d−1)f 2 ⌉, where g and f denote the genus and the Frobenius number of S. The case d = 2 is a problem proposed by Robles-Pérez, Rosales, and Vasco. Furthermore, we find th...
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If S is a numerical semigroup with embedding dimension equal to three whose minimal generators are pairwise relatively prime numbers, then S = 〈a, b, cb − da〉 with a, b, c, d positive integers such that gcd(a, b) = gcd(a, c) = gcd(b, d) = 1, c ∈ {2, . . . , a− 1}, and a < b < cb− da. In this paper we give formulas, in terms of a, b, c, d, for the genus, the Frobenius number, and the set of pseu...
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We conjecture a Fibonacci-like property on the number of numerical semigroups of a given genus. Moreover we conjecture that the associated quotient sequence approaches the golden ratio. The conjecture is motivated by the results on the number of semigroups of genus at most 50. The Wilf conjecture has also been checked for all numerical semigroups with genus in the same range.
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Combinatorics on multisets is used to deduce new upper and lower bounds on the number of numerical semigroups of each given genus, significantly improving existing ones. In particular, it is proved that the number ng of numerical semigroups of genus g satisfies 2Fg 6 ng 6 1 + 3 · 2 , where Fg denotes the gth Fibonacci number.
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ژورنال
عنوان ژورنال: Semigroup Forum
سال: 2022
ISSN: ['0037-1912', '1432-2137']
DOI: https://doi.org/10.1007/s00233-022-10298-y