Sparse Numerical Semigroups

Munuera, Carlos; Torres, Fernando; Villanueva, J.

doi:10.1007/978-3-642-02181-7_3

Cited by 10 publications

(7 citation statements)

References 12 publications

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“…For even values of κ,the previous result had been stated and proved by Munuera, Villanueva and Torres [MTV,Theorem 2.9 (3)] by means of a completely diverse approach.…”

Section: ])mentioning

confidence: 60%

“…Another class of sparse semigroups are Arf semigroups [MTV,Corollary 2.2]. We recall that a numerical semigroup H is an Arf semigroup if n i + n j − n k ∈ H, for i ≥ j ≥ k (see [BDF,Theorem I.3.4] for fifteen alternative characterizations of Arf semigroups, among which we call attention to the following: H is an Arf semigroup if and only if 2n i − n j ∈ H, for all i ≥ j ≥ 1).…”

Section: Sparse Semigroupsmentioning

confidence: 99%

“…We recall that a numerical semigroup H is an Arf semigroup if n i + n j − n k ∈ H, for i ≥ j ≥ k (see [BDF,Theorem I.3.4] for fifteen alternative characterizations of Arf semigroups, among which we call attention to the following: H is an Arf semigroup if and only if 2n i − n j ∈ H, for all i ≥ j ≥ 1). There are, however, sparse semigroups that are not Arf see Remark 3.10 or [MTV,Example 2.3…”

Section: Sparse Semigroupsmentioning

confidence: 99%

See 2 more Smart Citations

On the structure of numerical sparse semigroups and applications to Weierstrass points

Contiero

Moreira

Veloso

2015

Journal of Pure and Applied Algebra

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In this work, we are concerned with the structure of sparse semigroups and some applications of them to Weierstrass points. We manage to describe, classify and find an upper bound for the genus of sparse semigroups. We also study the realization of some sparse semigroups as Weierstrass semigroups. The smoothness property of monomial curves associated to (hyper)ordinary semigroups presented by Pinkham and Rim-Vitulli, and the results on double covering of curves by Torres are crucial in this.

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“…For even values of κ,the previous result had been stated and proved by Munuera, Villanueva and Torres [MTV,Theorem 2.9 (3)] by means of a completely diverse approach.…”

Section: ])mentioning

confidence: 60%

Section: Sparse Semigroupsmentioning

confidence: 99%

Section: Sparse Semigroupsmentioning

confidence: 99%

See 1 more Smart Citation

On the structure of numerical sparse semigroups and applications to Weierstrass points

Contiero

Moreira

Veloso

2015

Journal of Pure and Applied Algebra

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“…For further work on Arf numerical semigroups and generalizations we refer the reader to [2,61,13,46]. For results on Arf semigroups related to coding theory, see [4,17].…”

Section: Arf Numerical Semigroupsmentioning

confidence: 99%

“…Consequently, Arf semigroups are sparse semigroups [46], that is, there are no two non-gaps in a row smaller than the conductor.…”

Section: Example 15 It Is Easy To Check That the Weierstrass Semigrou...mentioning

confidence: 99%

Numerical Semigroups and Codes

Bras-Amorós¹

2013

Algebraic Geometry Modeling in Information Theory

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A numerical semigroup is a subset of N containing 0, closed under addition and with finite complement in N. An important example of numerical semigroup is given by the Weierstrass semigroup at one point of a curve. In the theory of algebraic geometry codes, Weierstrass semigroups are crucial for defining bounds on the minimum distance as well as for defining improvements on the dimension of codes. We present these applications and some theoretical problems related to classification, characterization and counting of numerical semigroups.Notice that a symmetric numerical semigroup can not be pseudo-symmetric. Next lemma as well as its proof is analogous to Lemma 10. Lemma 12.A numerical semigroup Λ with odd conductor c is pseudo-symmetric if and only if for any non-negative integer i different from (c − 1)/2, if i is a gap, then c − 1 − i is a non-gap. 9

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A decomposition of partitions and numerical sets

Karakas

Tutaş

2020

Semigroup Forum

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Sparse Numerical Semigroups

Cited by 10 publications

References 12 publications

On the structure of numerical sparse semigroups and applications to Weierstrass points

On the structure of numerical sparse semigroups and applications to Weierstrass points

Numerical Semigroups and Codes

A decomposition of partitions and numerical sets

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