Composition tableaux and further combinatorial concepts

2013 ◽  
pp. 51-62
Author(s):  
Kurt Luoto ◽  
Stefan Mykytiuk ◽  
Stephanie van Willigenburg
Keyword(s):  
Composition Tableaux

scholarly journals Permuted composition tableaux, 0-Hecke algebra and labeled binary trees

2019 ◽  
Vol 161 ◽  
pp. 420-452
Author(s):  
V. Tewari ◽  
S. van Willigenburg
Keyword(s):  
Hecke Algebra ◽  
Binary Trees ◽  
Composition Tableaux

scholarly journals Modules of the 0-Hecke algebra arising from standard permuted composition tableaux

2021 ◽  
Vol 179 ◽  
pp. 105389
Author(s):  
Seung-Il Choi ◽  
Young-Hun Kim ◽  
Sun-Young Nam ◽  
Young-Tak Oh
Keyword(s):  
Hecke Algebra ◽  
Composition Tableaux

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

10.37236/4976 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Vasu Tewari
Keyword(s):  
Schur Functions ◽  
Jeu De Taquin ◽  
Natural Operator ◽  
Quasisymmetric Schur Functions ◽  
Maximal Chains ◽  
Noncommutative Schur Functions ◽  
Composition Tableaux

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.

scholarly journals Quasisymmetric Schur functions and modules of the $0$-Hecke algebra

2014 ◽  
Vol DMTCS Proceedings vol. AT,... (Proceedings) ◽  
Author(s):  
Vasu Tewari ◽  
Stephanie van Willigenburg
Keyword(s):  
Schur Functions ◽  
Hecke Algebra ◽  
Bruhat Order ◽  
Schur Function ◽  
Quasisymmetric Functions ◽  
Weak Bruhat Order ◽  
International Audience ◽  
Quasisymmetric Schur Functions ◽  
Hecke Modules ◽  
Composition Tableaux

International audience We define a $0$-Hecke action on composition tableaux, and then use it to derive $0$-Hecke modules whose quasisymmetric characteristic is a quasisymmetric Schur function. We then relate the modules to the weak Bruhat order and use them to derive a new basis for quasisymmetric functions. We also classify those modules that are tableau-cyclic and likewise indecomposable. Finally, we develop a restriction rule that reflects the coproduct of quasisymmetric Schur functions. Nous définissons une action $0$-Hecke sur les tableaux de composition, et ensuite nous l’utilisons pour dériver les modules $0$-Hecke dont la caractéristique quasi-symétrique est une fonction de Schur quasi-symétrique. Nous mettons les modules en relation avec l’ordre de Bruhat faible et les utilisons pour dériver une nouvelle base pour les fonctions quasi-symétriques. Nous classons aussi ces modules qui sont tableau-cycliques et aussi indécomposable. Enfin, nous développons une règle de restriction qui reflète le coproduit des fonctions de Schur quasi-symétriques.

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