Backward jeu de taquin slides for composition tableaux and a noncommutative Pieri rule (Q2260614)

Summary: We give a backward jeu de taquin slide analogue on semistandard reverse composition tableaux. These tableaux were first studied by \textit{J. Haglund} et al. [J. Comb. Theory, Ser. A 118, No. 2, 463--490 (2011; Zbl 1229.05270)] 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.