Numerical semigroups with distances no admisible between gaps greater than its multiplicity | Synapse
March 3, 2026Open Access
Numerical semigroups with distances no admisible between gaps greater than its multiplicity
Key Points
Numerical semigroups exhibit properties that restrict distances between defined gaps and their multiplicity.
If x > y, the difference x-y must not belong to a designated subset A of positive integers.
Exploration involves nonempty subsets of positive integers and their implications on numerical semigroups.
Findings indicate that certain mathematical structures could be developed based on these gap restrictions.
Abstract
Let A pabe a nonempty subset of positive integers. In this paper we study the set of numerical semigroups that fulfill: if x, y ⊆ ℕS and x > y > min (S0), then x-y ∉ A.