The Article A View On Symmetric Numerical Semigroups

In this paper, we will give some results about the symmetric numerical semigroups such that Sk=<7,7k+4> where k is integer number.. Also, we will obtain Arf closure of these symmetric numerical semigroups.

Almost symmetric numerical semigroups with given Frobenius number and type

We give two algorithmic procedures to compute the whole set of almost symmetric numerical semigroups with fixed Frobenius number and type, and the whole set of almost symmetric numerical semigroups with fixed Frobenius number. Our algorithms allow to compute the whole set of almost symmetric numerical semigroups with fixed Frobenius number with similar or even higher efficiency that the known ones. They have been implemented in the GAP [The GAP Group, GAP — Groups, Algorithms and Programming, Version 4.8.6; 2016, https://www.gap-system.org ] package NumericalSgps [M. Delgado and P. A. García-Sánchez and J. Morais, “numericalsgps”: A GAP package on numerical semigroups, https://github.com/gap-packages/numericalsgps ].

Gluing semigroups and strongly indispensable free resolutions

We study strong indispensability of minimal free resolutions of semigroup rings focusing on the operation of gluing used in the literature to take examples with a special property and produce new ones. We give a naive condition to determine whether gluing of two semigroup rings has a strongly indispensable minimal free resolution. As applications, we determine simple gluings of [Formula: see text]-generated non-symmetric, [Formula: see text]-generated symmetric and pseudo symmetric numerical semigroups as well as obtain infinitely many new complete intersection semigroups of any embedding dimensions, having strongly indispensable minimal free resolutions.

Parametrizing numerical semigroups with multiplicity up to 5

In this work, we give parametrizations in terms of the Kunz coordinates of numerical semigroups with multiplicity up to [Formula: see text]. We also obtain parametrizations of MED semigroups, symmetric and pseudo-symmetric numerical semigroups with multiplicity up to [Formula: see text]. These parametrizations also lead to formulas for the number of numerical semigroups, the number of MED semigroups and the number of symmetric and pseudo-symmetric numerical semigroups with multiplicity up to [Formula: see text] and given conductor.