Rectangular Schroder Parking Functions Combinatorics

TL;DR

This paper explores the combinatorics of Schroder paths within rectangles, providing explicit enumeration formulas and introducing a Schroder version of (m,n)-parking functions along with their (q,t)-analogs.

Contribution

It introduces a new Schroder path framework in rectangles and develops enumeration formulas and parking function analogs related to (m,n)-Dyck paths.

Findings

Explicit formulas for Schroder path enumeration

A Schroder version of (m,n)-parking functions

Development of (q,t)-analogs for these structures

Abstract

We study Schroder paths drawn in a (m,n) rectangle, for any positive integers m and n. We get explicit enumeration formulas, closely linked to those for the corresponding (m,n)-Dyck paths. Moreover we study a Schroder version of (m,n)-parking functions, and associated (q,t)-analogs.