Geodesic
On certain families of sparse numerical semigroups with Frobenius number even
Algebra and discrete mathematics, Tome 27 (2019) no. 1, pp. 99-116.

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This paper is about sparse numerical semigroups and applications in the Weierstrass semigroups theory. We describe and find the genus of certain families of sparse numerical semigroups with Frobenius number even and we also study the realization of the elements on these families as Weierstrass semigroups.
Keywords: Arf numerical semigroup, numerical semigroup, sparse numerical semigroup, Weierstrass semigroup, weight of numerical semigroup. 
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Guilherme Tizziotti; Juan Villanueva. On certain families of sparse numerical semigroups with Frobenius number even. Algebra and discrete mathematics, Tome 27 (2019) no. 1, pp. 99-116. http://geodesic.mathdoc.fr/item/ADM_2019_27_1_a10/

[1] C. Arf, “Une interpretation algébrique de la suite des ordres de multiplicité dúne branche algébrique”, Proc. London Math. Soc., 50 (1949), 256–287 | MR

[2] V. Barucci, D. E. Dobbs and M. Fontana, Maximality properties in numerical semigroups and applications to one-dimensional analytically irreducible local domains, Mem. Amer. Math. Soc., 125, 1997 | MR

[3] M. Bras-Amorós, “Acute semigroups, the order bound on the minimum distance, and the Feng-Rao improvement”, IEEE Trans. Inform. Theory, 50:6 (2004), 1282–1289 | DOI | MR | Zbl

[4] R. O. Buchweitz, On Zariski's criterion for equisingularity and nonsmoothable monomial curves, Preprint 115, Univ. of Hannover, 1980 | Zbl

[5] A. Campillo, J. I. Farrán and C. Munuera, “On the parameters of algebraic-geometry codes related to Arf semigroups”, IEEE Trans. Inform. Theory, 46:7 (2000), 2634–2638 | DOI | MR | Zbl

[6] A. Contiero, C. G. T. A. Moreira and P. M. Veloso, “On the structure of numerical sparse semigroups and applications to Weierstrass points”, Journal of Pure and Applied Algebra, 219 (2015), 3946-?3957 | DOI | MR | Zbl

[7] D. Eisenbud and J. Harris, “Existence, decomposition and limits of certain Weierstrass points”, Invent. Math., 87 (1987), 495–515 | DOI | MR | Zbl

[8] J. Komeda, “On Weierstrass points whose first non-gaps are four”, J. Reine Angew. Math., 341 (1983), 237–270 | MR

[9] J. Komeda, “On primitive Schubert indices of genus $g$ and weight $g-1$”, J. Math. Soc. Japan, 43:3 (1991), 437–445 | DOI | MR | Zbl

[10] J. Komeda, “On the existence of Weierstrass points whose first non-gaps are five”, Manuscripta Math., 76:2 (1992), 193–211 | DOI | MR | Zbl

[11] J. Komeda, “On the existence of Weierstrass gap sequences on curves of genus $\leq 8$”, J. Pure Appl. Algebra, 97 (1994), 51–71 | DOI | MR | Zbl

[12] J. Komeda, “Double coverings of curves and non-Weierstrass semigroups”, Commun. Algebra, 41 (2013), 312–324 | DOI | MR | Zbl

[13] C. Maclachlan, “Weierstrass points on compact Riemann surfaces”, J. London Math. Soc. (2), 3 (1971), 722–724 | DOI | MR | Zbl

[14] C. Munuera, F. Torres and J. Villanueva, “Sparse Numerical Semigroups”, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, Lecture Notes in Computer Science, 5527, Springer-Verlag, Berlin–Heilderberg, 2009, 23–31 | DOI | MR | Zbl

[15] G. Oliveira, “Weierstrass semigroups and the canonical ideal of non-trigonal curves”, Manuscripta Math., 71 (1991), 431–450 | DOI | MR | Zbl

[16] J. C. Rosales, P. A. García-Sánchez, J. I. García-García and M. B. Branco, “Arf Numerical Semigroups”, Journal of Algebra, 276 (2004), 3–12 | DOI | MR | Zbl

[17] J. C. Rosales and P. A. García-Sánchez, Numerical Semigroups, Developments in Mathematics, Springer-Verlag, New York, 2012 | MR

[18] G. Tizziotti and J. Villanueva, “On $\kappa$-sparse numerical semigroups”, Journal of Algebra and Its Applications, 17:11 (2018) | DOI | MR | Zbl

[19] F. Torres, “Weierstrass points and double coverings of curves with applications: Symmetric numerical semigroups which cannot be realized as Weierstrass semigroups”, Manuscripta Math., 83 (1994), 39–58 | DOI | MR | Zbl

[20] J. Villanueva, Semigrupos fracamente de Arf e pesos de semigrupos, Ph.D. Thesis, UNICAMP, 2008