Minimal orbits of promotion

TL;DR

This paper establishes a bijection linking symmetric group elements to specific Young tableaux with a promotion order, revealing new combinatorial structures and symmetries.

Contribution

It introduces a novel bijection between the symmetric group and Young tableaux with a promotion order of n, connecting algebraic and combinatorial objects.

Findings

Bijection between S_n and certain Young tableaux

Characterization of tableaux with promotion order n

New insights into combinatorial symmetry structures

Abstract

We give a bijection between the symmetric group S_n, and the set of standard Young tableaux of rectangular shape m^n, m<=n, that have order n under jeu de taquin promotion.