Numerical semigroups with a given set of pseudo-Frobenius numbers
M. Delgado, P. A. Garc\'ia-S\'anchez, A. M. Robles-P\'erez
TL;DR
This paper introduces a method to determine whether a given set of integers can be the pseudo-Frobenius numbers of a numerical semigroup and to find all such semigroups if they exist.
Contribution
It provides a novel procedure for identifying and constructing numerical semigroups based on specified pseudo-Frobenius numbers.
Findings
A detection algorithm for pseudo-Frobenius sets
Computation of all semigroups with a given pseudo-Frobenius set
Characterization of pseudo-Frobenius number sets
Abstract
The pseudo-Frobenius numbers of a numerical semigroup are those gaps of the numerical semigroup that are maximal for the partial order induced by the semigroup. We present a procedure to detect if a given set of integers is the set of pseudo-Frobenius numbers of a numerical semigroup and, if so, to compute the set of all numerical semigroups having this set as set of pseudo-Frobenius numbers.
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