Parity numerical semigroups

Year 2020, Volume: 49 Issue: 3, 1067 - 1075, 02.06.2020

María ángeles Moreno Frıas , José Carlos Rosales

https://doi.org/10.15672/hujms.548289

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.

Keywords

Embedding dimension, Frobenius Number, Genus, Multiplicity, numerical semigroup

References

• [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.