scholarly journals Noncommutative Schur functions and their applications

2006 ◽  
Vol 306 (10-11) ◽  
pp. 1080-1096 ◽  
Author(s):  
Sergey Fomin ◽  
Curtis Greene
Keyword(s):  
Schur Functions ◽  
Noncommutative Schur Functions

scholarly journals Noncommutative schur functions and their applications

1998 ◽  
Vol 193 (1-3) ◽  
pp. 179-200 ◽  
Author(s):  
Sergey Fomin ◽  
Curtis Greene
Keyword(s):  
Schur Functions ◽  
Noncommutative Schur Functions

scholarly journals The shifted plactic monoid (extended abstract)

2009 ◽  
Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽  
Author(s):  
Luis Serrano
Keyword(s):  
Schur Functions ◽  
Plactic Monoid ◽  
Combinatorial Derivation ◽  
International Audience ◽  
Noncommutative Schur Functions

International audience We introduce a shifted analog of the plactic monoid of Lascoux and Schützenberger, the \emphshifted plactic monoid. It can be defined in two different ways: via the \emphshifted Knuth relations, or using Haiman's mixed insertion. Applications include: a new combinatorial derivation (and a new version of) the shifted Littlewood-Richardson Rule; similar results for the coefficients in the Schur expansion of a Schur P-function; a shifted counterpart of the Lascoux-Schützenberger theory of noncommutative Schur functions in plactic variables; a characterization of shifted tableau words; and more.

scholarly journals Skew quasisymmetric Schur functions and noncommutative Schur functions

2011 ◽  
Vol 226 (5) ◽  
pp. 4492-4532 ◽  
Author(s):  
C. Bessenrodt ◽  
K. Luoto ◽  
S. van Willigenburg
Keyword(s):  
Schur Functions ◽  
Quasisymmetric Schur Functions ◽  
Noncommutative Schur Functions

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 Noncommutative Schur functions, switchboards, and Schur positivity

2016 ◽  
Vol 23 (1) ◽  
pp. 727-766 ◽  
Author(s):  
Jonah Blasiak ◽  
Sergey Fomin
Keyword(s):  
Schur Functions ◽  
Noncommutative Schur Functions

Optimal Assembly of Systems Using Schur-Functions and Majorization.

1986 ◽  
Author(s):  
Emad El-Neweihi ◽  
Frank Proschan ◽  
Jayaram Sethuraman
Keyword(s):  
Schur Functions ◽  
Optimal Assembly

scholarly journals Proof of a positivity conjecture on Schur functions

2013 ◽  
Vol 120 (3) ◽  
pp. 644-648 ◽  
Author(s):  
William Y.C. Chen ◽  
Anne X.Y. Ren ◽  
Arthur L.B. Yang
Keyword(s):  
Schur Functions
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