Backward jeu de taquin slides for composition tableaux and a noncommutative Pieri rule

TL;DR

This paper introduces a backward jeu de taquin slide algorithm for semistandard reverse composition tableaux, leading to a new composition operator, a poset structure, and a noncommutative Pieri rule for Schur functions.

Contribution

It develops a novel backward jeu de taquin slide method on reverse composition tableaux, defining the jdt operator and establishing a new poset structure with applications to noncommutative Schur functions.

Findings

Defined the jdt operator on compositions

Established a new poset structure on compositions

Derived a noncommutative Pieri rule for Schur functions

Abstract

We give a backward jeu de taquin slide analogue on semistandard reverse composition tableaux. These tableaux were first studied by Haglund, Luoto, Mason and van Willigenburg when defining quasisymmetric Schur functions. Our algorithm for performing backward jeu de taquin slides on semistandard reverse composition tableaux results in a natural operator on compositions that we call the jdt operator. This operator in turn gives rise to a new poset structure on compositions whose maximal chains we enumerate. As an application, we also give a noncommutative Pieri rule for noncommutative Schur functions that uses the jdt operators.