scholarly journals Ordered set partitions and the $0$-Hecke algebra

2018 ◽  
Vol 1 (1) ◽  
pp. 47-80 ◽  
Author(s):  
Jia Huang ◽  
Brendon Rhoades
Keyword(s):  
Ordered Set ◽  
Hecke Algebra ◽  
Set Partitions ◽  
Ordered Set Partitions

Euler–Mahonian Statistics on Ordered Set Partitions

2008 ◽  
Vol 22 (3) ◽  
pp. 1105-1137 ◽  
Author(s):  
Masao Ishikawa ◽  
Anisse Kasraoui ◽  
Jiang Zeng
Keyword(s):  
Ordered Set ◽  
Set Partitions ◽  
Ordered Set Partitions ◽  
Mahonian Statistics

scholarly journals An extension of MacMahon's equidistribution theorem to ordered set partitions

2015 ◽  
Vol 134 ◽  
pp. 242-277 ◽  
Author(s):  
Jeffrey B. Remmel ◽  
Andrew Timothy Wilson
Keyword(s):  
Ordered Set ◽  
Set Partitions ◽  
Ordered Set Partitions

scholarly journals Hall-Littlewood polynomials and a Hecke action on ordered set partitions

2019 ◽  
Vol 147 (5) ◽  
pp. 1839-1850
Author(s):  
Jia Huang ◽  
Brendon Rhoades ◽  
Travis Scrimshaw
Keyword(s):  
Ordered Set ◽  
Set Partitions ◽  
Littlewood Polynomials ◽  
Ordered Set Partitions

scholarly journals Pattern Avoidance in Ordered Set Partitions

2014 ◽  
Vol 18 (3) ◽  
pp. 429-445 ◽  
Author(s):  
Anant Godbole ◽  
Adam Goyt ◽  
Jennifer Herdan ◽  
Lara Pudwell
Keyword(s):  
Ordered Set ◽  
Pattern Avoidance ◽  
Set Partitions ◽  
Ordered Set Partitions

scholarly journals Euler–Mahonian statistics on ordered set partitions (II)

2009 ◽  
Vol 116 (3) ◽  
pp. 539-563 ◽  
Author(s):  
Anisse Kasraoui ◽  
Jiang Zeng
Keyword(s):  
Ordered Set ◽  
Set Partitions ◽  
Ordered Set Partitions ◽  
Mahonian Statistics

scholarly journals Patterns in words of ordered set partitions

2019 ◽  
Vol 10 (3) ◽  
pp. 433-490
Author(s):  
Dun Qiu ◽  
Jeffrey Remmel
Keyword(s):  
Ordered Set ◽  
Set Partitions ◽  
Ordered Set Partitions

scholarly journals The Delta Conjecture

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
James Haglund ◽  
Jeffrey B. Remmel ◽  
Andrew Timothy Wilson
Keyword(s):  
Symmetric Function ◽  
Ordered Set ◽  
Macdonald Polynomials ◽  
Catalan Numbers ◽  
Set Partitions ◽  
Combinatorial Interpretations ◽  
Llt Polynomials ◽  
Ordered Set Partitions ◽  
International Audience ◽  
Tesler Matrices

International audience We conjecture two combinatorial interpretations for the symmetric function ∆eken, where ∆f is an eigenoperator for the modified Macdonald polynomials defined by Bergeron, Garsia, Haiman, and Tesler. Both interpretations can be seen as generalizations of the Shuffle Conjecture, a statement originally conjectured by Haglund, Haiman, Remmel, Loehr, and Ulyanov and recently proved by Carlsson and Mellit. We show how previous work of the second and third authors on Tesler matrices and ordered set partitions can be used to verify several cases of our conjectures. Furthermore, we use a reciprocity identity and LLT polynomials to prove another case. Finally, we show how our conjectures inspire 4-variable generalizations of the Catalan numbers, extending work of Garsia, Haiman, and the first author.

scholarly journals A Semigroup Approach to Wreath-Product Extensions of Solomon's Descent Algebras

10.37236/110 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Samuel K. Hsiao
Keyword(s):  
Symmetric Group ◽  
Wreath Product ◽  
Ordered Set ◽  
Semigroup Algebra ◽  
Arbitrary Group ◽  
Set Partitions ◽  
Semigroup Approach ◽  
Combinatorial Model ◽  
Ordered Set Partitions ◽  
Descent Algebras

There is a well-known combinatorial model, based on ordered set partitions, of the semigroup of faces of the braid arrangement. We generalize this model to obtain a semigroup ${\cal F}_n^G$ associated with $G\wr S_n$, the wreath product of the symmetric group $S_n$ with an arbitrary group $G$. Techniques of Bidigare and Brown are adapted to construct an anti-homomorphism from the $S_n$-invariant subalgebra of the semigroup algebra of ${\cal F}_n^G$ into the group algebra of $G\wr S_n$. The colored descent algebras of Mantaci and Reutenauer are obtained as homomorphic images when $G$ is abelian.

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