A short conceptual proof of Narayana's path-counting formula

TL;DR

This paper provides a concise conceptual proof of Narayana's path-counting formula by leveraging the Gessel-Viennot theorem, simplifying the understanding of lattice path enumeration within Young diagrams.

Contribution

It offers a direct, conceptual proof of Narayana's formula using the Gessel-Viennot theorem, enhancing theoretical understanding.

Findings

Narayana's formula derived from Gessel-Viennot theorem

Simplified proof of lattice path enumeration

Connection between Young diagrams and non-intersecting paths

Abstract

We deduce Narayana's formula for the number of lattice paths that fit in a Young diagram as a direct consequence of the Gessel-Viennot theorem on non-intersecting lattice paths.