Numerical Semigroups with a Given Frobenius Number and Some Fixed Gaps

Abstract

If P is a nonempty finite subset of positive integers, then (Formula presented.) In this work, we prove that (Formula presented.) is a covariety; therefore, we can arrange the elements of (Formula presented.) in the form of a tree. This fact allows us to present several algorithms, including one that calculates all the elements of (Formula presented.), another that obtains its maximal elements (with respect to the set inclusion order) and one more that computes the elements of (Formula presented.) that cannot be expressed as an intersection of two elements of (Formula presented.) that properly contain it.