Enumeration of area-weighed Dyck paths with restricted height

TL;DR

This paper derives explicit formulas for q-orthogonal polynomials that count area-weighted Dyck paths with height restrictions, advancing combinatorial enumeration techniques.

Contribution

It provides new explicit expressions for q-orthogonal polynomials related to restricted Dyck path enumeration.

Findings

Explicit formulas for q-orthogonal polynomials derived

Enumeration of area-weighted Dyck paths with height restrictions achieved

Enhanced understanding of combinatorial structures involving Dyck paths

Abstract

We derive explicit expressions for $q$-orthogonal polynomials arising in the enumeration of area-weighted Dyck paths with restricted height.