2017
DOI: 10.1142/s0219498817502097
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Parametrizing Arf numerical semigroups

Abstract: Communicated by R. WiegandWe present procedures to calculate the set of Arf numerical semigroups with given genus, given conductor and given genus and conductor. We characterize the Kunz coordinates of an Arf numerical semigroup. We also describe Arf numerical semigroups with fixed Frobenius number and multiplicity up to 7.

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Cited by 22 publications
(31 citation statements)
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“…By focusing on the numerical properties that a sequence has to satisfy to be a multiplicity sequence, it is possible to study the Arf numerical semigroups with a combinatorial approach without referring to the ring theory context. In the first section of this paper we present a new procedure to compute all Arf numerical semigroups S with a prescribed genus, that is the cardinality of N \ S (this problem was already addressed in [6]). Keywords: Arf numerical semigroup, good semigroup, algebroid curve, genus.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…By focusing on the numerical properties that a sequence has to satisfy to be a multiplicity sequence, it is possible to study the Arf numerical semigroups with a combinatorial approach without referring to the ring theory context. In the first section of this paper we present a new procedure to compute all Arf numerical semigroups S with a prescribed genus, that is the cardinality of N \ S (this problem was already addressed in [6]). Keywords: Arf numerical semigroup, good semigroup, algebroid curve, genus.…”
Section: Introductionmentioning
confidence: 99%
“…In [6] it is presented an algorithm for the computation of the set of the Arf numerical semigroups with a given genus. In this section we give a new procedure for the computation of such a set that appeared to be faster when implemented in GAP.…”
Section: Introductionmentioning
confidence: 99%
“…In Section 1, we firstly recall some definitions and properties concerning the numerical semigroups. Then we address the problem, already studied in [4], of finding the set of the multiplicity sequences of all the Arf numerical semigroups with a fixed conductor. In [4] the authors found a recursive algorithm for the computation of such a set, while in this section it is presented a non recursive procedure to determine it, that is faster than the previous one, when used for large value of the conductor.…”
Section: Introductionmentioning
confidence: 99%
“…1 An algorithm for Cond(n) where n ∈ N In [4] it is presented an algorithm for the computation of the set of the Arf numerical semigroups with a given conductor. In this section we give a new procedure for the computation of such a set that appeared to be faster when implemented in GAP.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation