A class of numerical semigroups defined by Kunz and Waldi — Their principal matrices and structure

In this paper, we explore a class of numerical semigroups initiated by Kunz and Waldi containing two coprime numbers [Formula: see text], 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 [Formula: see text] and [Formula: see text] 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.