A Class of Numerical Semigroups Defined by Kunz and Waldo

In this paper, we explore a class of numerical semigroups initiated by Kunz and Waldi containing two coprime numbers $p < q$, which we call KW semigroups. We characterize KW numerical semigroups by their principal matrices. We present a necessary and sufficient criterion for a matrix to be the principal matrix of a KW semigroup. An explicit description of the minimal resolutions of numerical semigroups in the same class with small embedding dimensions 3 and 4 is given. We give a generalization of this notion to three dimensions using lattice paths under a plane and present some preliminary results and questions.