Backward jeu de taquin slides for composition tableaux and a noncommutative Pieri rule
The electronic journal of combinatorics, Tome 22 (2015) no. 1
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.
DOI :
10.37236/4976
Classification :
05E05, 05E10, 20C30
Mots-clés : jeu de taquin, noncommutative symmetric function, Schur function, tableau, Pieri rule
Mots-clés : jeu de taquin, noncommutative symmetric function, Schur function, tableau, Pieri rule
Affiliations des auteurs :
Vasu Tewari 1
@article{10_37236_4976,
author = {Vasu Tewari},
title = {Backward jeu de taquin slides for composition tableaux and a noncommutative {Pieri} rule},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {1},
doi = {10.37236/4976},
zbl = {1308.05105},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4976/}
}
Vasu Tewari. Backward jeu de taquin slides for composition tableaux and a noncommutative Pieri rule. The electronic journal of combinatorics, Tome 22 (2015) no. 1. doi: 10.37236/4976
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