Generalizing strong admissibility of patterns of numerical semigroups
Guangren Sun, Zhengjun Zhao · International Journal of Algebra and Computation · 2017
A homogeneous pattern is a linear multivariate polynomial without constant term. Bras-Amorós and García-Sánchez introduced the notion of pattern for numerical semigroups, which generalizes the definition of Arf numerical semigroups. The notion of pattern for numerical semigroups is extended in this paper into a family of homogeneous patterns [Formula: see text]. A numerical semigroup admitting a family of homogeneous patterns [Formula: see text] at [Formula: see text]-level is characterized. We pay our attention in this paper to the families with the action of some permutation groups, especially those consisting of certain partition stabilizers. Stable or sensitive patterns are focused on and we characterize them for several specific permutation groups.