scholarly journals Set-valued domino tableaux and shifted set-valued domino tableaux

2020 ◽  
Vol 13 (5) ◽  
pp. 721-746
Author(s):  
Florence Maas-Gariépy ◽  
Rebecca Patrias
Keyword(s):  
Domino Tableaux

scholarly journals Domino tableaux, Schützenberger involution, and the symmetric group action

2000 ◽  
Vol 225 (1-3) ◽  
pp. 15-24 ◽  
Author(s):  
Arkady Berenstein ◽  
Anatol N. Kirillov
Keyword(s):  
Symmetric Group ◽  
Group Action ◽  
Domino Tableaux

Skew Standard Domino Tableaux and Partial Motzkin Paths

2017 ◽  
Vol 21 (1) ◽  
pp. 43-71
Author(s):  
Ting-Yuan Cheng ◽  
Sen-Peng Eu ◽  
Tung-Shan Fu ◽  
Yi-Lin Lee
Keyword(s):  
Domino Tableaux ◽  
Motzkin Paths

scholarly journals Module structure of cells in unequal-parameter Hecke algebras

2010 ◽  
Vol 198 ◽  
pp. 23-45 ◽  
Author(s):  
Thomas Pietraho
Keyword(s):  
Weyl Group ◽  
Recent Work ◽  
Hecke Algebras ◽  
Module Structure ◽  
Domino Tableaux ◽  
Arbitrary Rank

AbstractA conjecture of Bonnafé, Geck, Iancu, and Lam parametrizes Kazhdan-Lusztig left cells for unequal-parameter Hecke algebras in type Bn by families of standard domino tableaux of arbitrary rank. Relying on a family of properties outlined by Lusztig and the recent work of Bonnafé, we verify the conjecture and describe the structure of each cell as a module for the underlying Weyl group.

scholarly journals Zonal polynomials and domino tableaux

1992 ◽  
Vol 99 (1-3) ◽  
pp. 3-15 ◽  
Author(s):  
Nantel Bergeron ◽  
Adriano M. Garsia
Keyword(s):  
Zonal Polynomials ◽  
Domino Tableaux

scholarly journals Components of the Springer fiber and domino tableaux

2004 ◽  
Vol 272 (2) ◽  
pp. 711-729 ◽  
Author(s):  
Thomas Pietraho
Keyword(s):  
Domino Tableaux ◽  
Springer Fiber

scholarly journals Cyclic Sieving and Plethysm Coefficients

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
David B Rush
Keyword(s):  
Fixed Points ◽  
Schur Function ◽  
Young Tableaux ◽  
Jeu De Taquin ◽  
Cyclic Action ◽  
Domino Tableaux ◽  
Ribbon Tableaux ◽  
International Audience ◽  
Cyclic Sieving ◽  
Element Set

International audience A combinatorial expression for the coefficient of the Schur function $s_{\lambda}$ in the expansion of the plethysm $p_{n/d}^d \circ s_{\mu}$ is given for all $d$ dividing $n$ for the cases in which $n=2$ or $\lambda$ is rectangular. In these cases, the coefficient $\langle p_{n/d}^d \circ s_{\mu}, s_{\lambda} \rangle$ is shown to count, up to sign, the number of fixed points of an $\langle s_{\mu}^n, s_{\lambda} \rangle$-element set under the $d^e$ power of an order $n$ cyclic action. If $n=2$, the action is the Schützenberger involution on semistandard Young tableaux (also known as evacuation), and, if $\lambda$ is rectangular, the action is a certain power of Schützenberger and Shimozono's <i>jeu-de-taquin</i> promotion.This work extends results of Stembridge and Rhoades linking fixed points of the Schützenberger actions to ribbon tableaux enumeration. The conclusion for the case $n=2$ is equivalent to the domino tableaux rule of Carré and Leclerc for discriminating between the symmetric and antisymmetric parts of the square of a Schur function. Une expression combinatoire pour le coefficient de la fonction de Schur $s_{\lambda}$ dans l’expansion du pléthysme $p_{n/d}^d \circ s_{\mu}$ est donné pour tous $d$ que disent $n$, dans les cas où $n=2$, ou $\lambda$ est rectangulaire. Dans ces cas, le coefficient $\langle p_{n/d}^d \circ s_{\mu}, s_{\lambda} \rangle$ se montre à compter, où l’on ignore le signe, le nombre des point fixés d’un ensemble de $\langle s_{\mu}^n, s_{\lambda} \rangle$ éléments sous la puissance $d^e$ d’une action cyclique de l’ordre $n$. Si $n=2$, l’action est l’involution de Schützenberger sur les tableaux semi-standard de Young (aussi connu sous le nom des évacuations), et si $\lambda$ est rectangulaire, l’action est une certaine puissance de l’avancement jeu-de-taquin de Schützenberger et Shimozono.Ce travail étend les résultats de Stembridge et Rhoades, liant les point fixés des actions de Schützenberger aux tableaux de ruban. Pour le cas $n=2$ , la conclusion est équivalent à la règle des tableaux de dominos de Carré et Leclerc, qui distingue entre les parties symétriques et asymétriques du carré d’une fonction de Schur.

scholarly journals Plactic relations for $r$-domino tableaux

10.37236/2042 ◽  
2012 ◽  
Vol 19 (1) ◽  
Author(s):  
Müge Taşkin
Keyword(s):  
Equivalence Relation ◽  
Type B ◽  
Domino Tableaux ◽  
Signed Permutations

The work of C. Bonnafé, M.Geck, L. Iancu and T. Lam shows through two conjectures that $r$-domino tableaux have an important role in Kazhdan-Lusztig theory of type $B$ with unequal parameters. In this paper we provide plactic relations on signed permutations which determine whether two given signed permutations have the same insertion $r$-domino tableaux in Garfinkle's algorithm. Moreover, we show that a particular extension of these relations can describe Garfinkle's equivalence relation on $r$-domino tableaux which is given through the notion of open cycles. With these results we enunciate the conjectures of Bonnafé et al. and provide necessary tools for their proofs.

scholarly journals Module structure of cells in unequal-parameter Hecke algebras

2010 ◽  
Vol 198 ◽  
pp. 23-45
Author(s):  
Thomas Pietraho
Keyword(s):  
Weyl Group ◽  
Recent Work ◽  
Hecke Algebras ◽  
Module Structure ◽  
Domino Tableaux ◽  
Arbitrary Rank

AbstractA conjecture of Bonnafé, Geck, Iancu, and Lam parametrizes Kazhdan-Lusztig left cells for unequal-parameter Hecke algebras in typeBnby families of standard domino tableaux of arbitrary rank. Relying on a family of properties outlined by Lusztig and the recent work of Bonnafé, we verify the conjecture and describe the structure of each cell as a module for the underlying Weyl group.

scholarly journals Skew domino Schensted algorithm and sign-imbalance

2008 ◽  
Vol DMTCS Proceedings vol. AJ,... (Proceedings) ◽  
Author(s):  
Jang Soo Kim
Keyword(s):  
Generating Function ◽  
Weighted Sum ◽  
Domino Tableaux ◽  
Spin Property ◽  
International Audience ◽  
Comme Application ◽  
Special Case

International audience Using growth diagrams, we define a skew domino Schensted algorithm which is a domino analogue of the "Robinson-Schensted algorithm for skew tableaux'' due to Sagan and Stanley. The color-to-spin property of Shimozono and White is extended. As an application, we give a simple generating function for a weighted sum of skew domino tableaux whose special case is a generalization of Stanley's sign-imbalance formula. The generating function gives a method to calculate the generalized sign-imbalance formula. Nous définissons, à partir de diagrammes de croissances, un algorithme de Schensted pour les dominos gauches. Cet algorithme est un analogue de l'algorithme de Schensted pour les tableaux gauches dû à Sagan et Stanley. Nous généralisons la propriété couleur-à-spin de Shimozono et White. Comme application, nous présentons une fonction génératrice simple pour une somme pondérée de tableaux de dominos gauches qui, dans un cas particulier, généralise la formule de "sign-imbalance'' de Stanley. La fonction génératrice donne aussi lieu à une méthode permettant de calculer la formule de "sign-imbalance''.

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