Bijections for an identity of Young Tableaux

TL;DR

This paper introduces a bijection linking specific Young tableaux configurations, simplifying the understanding of their combinatorial relationships and providing a new perspective on tableau enumeration.

Contribution

It presents a novel bijection between two classes of Young tableaux, expanding combinatorial tools for tableau analysis.

Findings

Establishes a bijection between tableaux with 2n cells and at most two rows and pairs of tableaux with n+1 cells.

Provides a new combinatorial interpretation of Young tableaux identities.

Enhances methods for counting and relating Young tableaux configurations.

Abstract

We present an elegant bijection between standard Young tableaux with 2n cells and at most two rows, and pairs of standard Young tableaux of the same shape, with n+1 cells, where only the top row can have more than one cell.