The Half-Perimeter Generating Function of Gated and Wicketed Ferrers diagrams

TL;DR

This paper proves that the half-perimeter generating functions for Wicketed and Gated Ferrers diagrams are algebraic, revealing a connection to Catalan numbers, using the umbral transfer matrix method.

Contribution

It introduces an algebraic characterization of the generating functions for these diagrams and links the Wicketed Ferrers diagrams to Catalan numbers.

Findings

The generating functions are algebraic.

Wicketed Ferrers diagrams relate to Catalan numbers.

Methodology involves umbral transfer matrix technique.

Abstract

We show that the half-perimeter generating functions for the number of Wicketed and Gated Ferrers diagrams is algebraic. Furthermore, the generating function of the Wicketed Ferrers diagrams is closely related to the generating function of the Catalan numbers. The methodology of the experimentation as well as the proof is the umbral transfer matrix method.