Resumen de Positive Definite Kernels and Lattice Paths

Tiberiu Constantinescu, Nermine El-Sissi

• In this paper, we explore the structure of positive definite kernels on the set of non-negative integers in terms of operator models. Particularly, we introduce two models, one of a Hessenberg type and another that we call ¿near tridiagonal.¿ These models produce two distinct parametrizations of the kernels. We also describe the combinatorial nature of these parametrizations in terms of lattice paths of Dyck and Lukasiewicz types.