Nonhomogeneous patterns on numerical semigroups
Abstract
Patterns on numerical semigroups are multivariate linear polynomials, and they are said to be admissible if there exists a numerical semigroup such that evaluated at any nonincreasing sequence of elements of the semigroup gives integers belonging to the semigroup. In a first approach, only homogeneous patterns where analized. In this contribution we study conditions for an eventually non-homogeneous pattern to be admissible, and particularize this study to the case the independent term of the pattern is a multiple of the multiplicity of the semigroup. Moreover, for the so called strongly admissible patterns, the set of numerical semigroups admitting these patterns with fixed multiplicity form an -variety, which allows us to represent this set in a tree and to describe minimal sets of generators of the semigroups in the variety with respect to the pattern. Furthermore, we characterize strongly admissible patterns having a finite associated tree.
Cite
@article{arxiv.1211.0895,
title = {Nonhomogeneous patterns on numerical semigroups},
author = {Maria Bras-Amorós and Pedro A. García-Sánchez and Albert Vico-Oton},
journal= {arXiv preprint arXiv:1211.0895},
year = {2012}
}