Dual Immaculate Quasisymmetric Functions Expand Positively into Young Quasisymmetric Schur Functions

International audience We describe a combinatorial formula for the coefficients when the dual immaculate quasisymmetric func- tions are decomposed into Young quasisymmetric Schur functions. We prove this using an analogue of Schensted insertion. We also provide a Remmel-Whitney style rule to generate these coefficients algorithmically.

Backward Jeu de Taquin Slides for Composition Tableaux and a Noncommutative Pieri Rule

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.