A Class of Numerical Semigroups Defined by Kunz and Waldi
arXiv:2405.00331
Abstract
In this paper, we explore a class of numerical semigroups initiated by Kunz and Waldi containing two coprime numbers , 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.
19 pages, 6 figures