Combinatorial properties of lattice paths

Abstract

We study a type of lattice path called a skew Dyck path which is a generalization of a Dyck path. Therefore we first introduce Dyck paths and study their enumeration according to various parameters such as number of peaks, valleys, doublerises and return steps. We study characteristics such as bijections with other combinatorial objects, involutions and statistics on skew Dyck paths. We then show enumerations of skew Dyck paths in relation to area, semi-base and semi-length. We finally introduce superdiagonal bargraphs which are associated with skew Dyck paths and enumerate them in relation to perimeter and area