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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 3

Parity numerical semigroups

María Ángeles MORENO-FRİAS
José Carlos ROSALES
Sayfa
1067–1075
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Also, we will study the maximal P-semigroups with a given Frobenius number as well as the P-semigroups with maximum embedding dimension.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:A numerical semigroup is parity (P-semigroup) if the sum of two consecutive elements of $S$ is odd.
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Temel Bulgular & Veri:In this paper we will order the P-semigroups creating a tree with root.
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Sonuç & Katkı:Also, we will study the maximal P-semigroups with a given Frobenius number as well as the P-semigroups with maximum embedding dimension.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Embedding dimension · Frobenius Number · Genus

Abstract

A numerical semigroup is parity (P-semigroup) if the sum of two consecutive elements of $S$ is odd. In this paper we will order the P-semigroups creating a tree with root. This ordering allows us to give some algorithms to build all the P-semigroups with a fixed genus and Frobenius number. Also, we will study the maximal P-semigroups with a given Frobenius number as well as the P-semigroups with maximum embedding dimension.

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Bu Makaleye Atıf Yap

MORENO-FRİAS, M. Á., ROSALES, J. C. (2022). Parity numerical semigroups. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 3, 1067–1075. https://ajindex.com/articles/529642

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Kaynakça (5)

  1. V. Barucci, D.E. Dobbs and M. Fontana, Maximality Properties in Numerical Semigroups and Applications to One-Dimensional Analitycally Irreducible Local Domains, Memoirs Amer. Math. Soc. 598, 1997
  2. M.A. Moreno-Frías and J.C. Rosales, Perfect numerical semigroups, Turkish J. Math. 43, 1742-1754, 2019
  3. J.C. Rosales, Principal ideals of numerical semigroups, Bull. Belg. Math. Soc. 10, 1-15, 2003
  4. J.C. Rosales and P.A. García-Sánchez, Numerical Semigroups, Developments in Mathematics, 20, Springer, New York, 2009
  5. J.C. Rosales, P.A. García-Sánchez, J.I. García-García and J.A. Jiménez-Madrid, The oversemigroups of a numerical semigroup, Semigroup Forum, 67, 145-158, 2003.