An exceptional equinumerosity of lattice paths and Young tableaux

TL;DR

This paper establishes a direct bijection demonstrating that certain families of plane lattice paths are equinumerous with specific sets of standard Young tableaux, revealing a new combinatorial equivalence.

Contribution

It introduces an explicit bijection proving the equinumerosity between lattice path families and Young tableaux, providing a new combinatorial insight.

Findings

Lattice path families are equinumerous with Young tableaux sets.

Explicit bijection constructed between the two combinatorial objects.

Reveals a new combinatorial equivalence in enumeration theory.

Abstract

We consider families $\mathcal{P}_n$ of plane lattice paths enumerated by Guy, Krattenthaler, and Sagan (1992). We show by explicit bijection that these families are equinumerous with the set $\mathrm{SYT}(n+2,2,1^n)$ of standard Young tableaux.