On the generators of a generalized numerical semigroup

Cisto, Carmelo; Failla, Gioia; Utano, Rosanna

doi:10.2478/auom-2019-0003

.blurhash-client-img { display: none !important; }

On the generators of a generalized numerical semigroup

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 27 (2019): Issue 1 (March 2019)

By: Carmelo Cisto, Gioia Failla and Rosanna Utano

Open Access

|Mar 2019

Abstract

We give a characterization on the sets A ⊆ ℕ^d such that the monoid generated by A is a generalized numerical semigroup (GNS) in ℕ^d. Furthermore we give a procedure to compute the hole set ℕ^d \ S, where S is a GNS, if a finite set of generators of S is known.

References

[1] Bras-Amorós, M.: Fibonacci-like behavior of the number of numerical semigroups of a given genus. Semigroup Forum 76, 379–384 (2008).10.1007/s00233-007-9014-8
Search in Google Scholar Back to article
[2] Bras-Amorós, M.: Bounds on the number of numerical semigroups of a given genus. J. Pure Appl.Algebra 213, 997–1001 (2009).10.1016/j.jpaa.2008.11.012
Search in Google Scholar Back to article
[3] Failla, G., Peterson, C., Utano, R.: Algorithms and basic asymptotics for generalized numerical semigroups in ℕ^d, Semigroup Forum 92(2), 460–473 (2016).10.1007/s00233-015-9690-8
Search in Google Scholar Back to article
[4] Fröberg, R., Gottlieb, C., Häggkvist, R.: On numerical semigroups. Semi-group Forum 35, 63–83 (1986/1987).10.1007/BF02573091
Search in Google Scholar Back to article
[5] Martino, I., Martino, L.: On the variety of linear recurrences and numerical semigroups. Semigroup Forum 88, 569–574 (2014).10.1007/s00233-013-9551-2
Search in Google Scholar Back to article
[6] Pisón-Casares, P., Vigneron-Tenorio, A.: ℕ-solutions to linear systems over ℤ. Linear Algebra Its Appl. 384, 135–154 (2004).10.1016/j.laa.2004.01.003
Search in Google Scholar Back to article
[7] Rosales, J.C.: On finitely generated submonoids of ℕ^k. Semigroup Forum 50, 251–262 (1995).10.1007/BF02573522
Search in Google Scholar Back to article
[8] J. C. Rosales, P. A. García-Sánchez, On Cohen-Macaulay and Gorenstein simplicial affine semigroups, Proc. Edinburgh Math. Soc. 41 (1998), 517–537.10.1017/S0013091500019866
Search in Google Scholar Back to article
[9] Rosales, J.C., García-Sánchez, P.A.: Numerical Semigroups, Developments in Mathematics, vol. 20. Springer, New York (2009).10.1007/978-1-4419-0160-6
Search in Google Scholar Back to article
[10] Rosales, J.C., García-Sánchez, P.A., García-García, J.I., Jiménez Madrid, J.A.: The oversemigroups of a numerical semigroup, Semigroup Forum 67(1), 145–158, (2003).10.1007/s00233-002-0007-3
Search in Google Scholar Back to article

DOI: https://doi.org/10.2478/auom-2019-0003 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

Journal RSS Feed

Language: English

Page range: 49 - 59

Submitted on: Jan 27, 2018

Accepted on: Apr 27, 2018

Published on: Mar 2, 2019

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Generalized numerical semigroup,

minimal generators

Related subjects:

Mathematics,

General mathematics

© 2019 Carmelo Cisto, Gioia Failla, Rosanna Utano, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Previous article Volume 27 (2019): Issue 1 (March 2019)Next article