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