Examines isolated gaps in non-perfect Arf numerical semigroups, revealing their structural relationships and implications.
Key Points
The research aims to analyze the structure and characteristics of isolated gaps in non-perfect Arf numerical semigroups and their relation to perfect Arf semigroups.
Analyzed the structural relationship between elements of non-perfect Arf numerical semigroups and their gap sets.
Characterized the position and behavior of isolated gaps in relation to the Frobenius number.
Investigated the union of Arf numerical semigroups with their isolated gaps.
The union of an Arf numerical semigroup with its isolated gaps forms a perfect Arf numerical semigroup.
Certain subsets of isolated gaps retain the non-perfect nature of the semigroups.
Clarified the transition between perfect and non-perfect Arf numerical semigroups through isolated gaps.