On isolated gaps in numerical semigroups

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

A numerical semigroup is said to be perfect if it does not contain any isolated gaps. In this paper, we will look at some basic properties of isolated gaps in numerical semigroups. In particular, we will see how they are related to elements of the Apéry set. We will use these properties to find all of the isolated gaps in a numerical semigroup of embedding dimension two and demonstrate a simple method of generating some examples of perfect numerical semigroups of embedding dimension three.

PDF

___

[1] Moreno Frías MA, Rosales JC. Perfect numerical semigroups. Turkish Journal of Mathematics 2019; 43 (3): 1742- 1754.
[2] Moreno-Frías MA, Rosales JC. Perfect numerical semigroups with embedding dimension three. Publ. Math. Debrecen 2020; 97 (1-2): 77-84.
[3] Niven I, Zuckerman HS, Montgomery HL. An Introduction to the Theory of Numbers. USA: John Wiley & Sons, 1991.
[4] Ramirez Alfonsin JL. The Diophantine Frobenius Problem. Oxford Lecture Series in Mathematics and its Applications 30. Oxford University Press, 2005.
[5] Rosales JC, García-Sánchez PA. Numerical Semigroups. Developments in Mathematics, Vol. 20. New York, NY, USA: Springer, 2009.