Bumping algorithm for set-valued shifted tableaux

International audience We present an insertion algorithm of Robinson–Schensted type that applies to set-valued shifted Young tableaux. Our algorithm is a generalization of both set-valued non-shifted tableaux by Buch and non set-valued shifted tableaux by Worley and Sagan. As an application, we obta...

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Bibliographic Details
Main Authors: Ikeda, Takeshi, Naruse, Hiroshi, Numata, Yasuhide
Other Authors: Okayama University of Science, Okayama University, Department of Mathematical Informatics (University of Tokyo), The University of Tokyo (UTokyo), Japan Science and Technology Agency (JST), Bousquet-Mélou, Mireille and Wachs, Michelle and Hultman, Axel
Format: Conference Object
Language:English
Published: HAL CCSD 2011
Subjects:
set-valued shifted tableaux
insertion
Robinson―Schensted
Pieri rule
K-theory
Schur Q-functions
[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Sagan
Iceland
Online Access:https://hal.inria.fr/hal-01215052
https://hal.inria.fr/hal-01215052/document
https://hal.inria.fr/hal-01215052/file/dmAO0147.pdf
Description
Summary:International audience We present an insertion algorithm of Robinson–Schensted type that applies to set-valued shifted Young tableaux. Our algorithm is a generalization of both set-valued non-shifted tableaux by Buch and non set-valued shifted tableaux by Worley and Sagan. As an application, we obtain a Pieri rule for a K-theoretic analogue of the Schur Q-functions. Nous présentons un algorithme d'insertion de Robinson–Schensted qui s'applique aux tableaux décalés à valeurs sur des ensembles. Notre algorithme est une généralisation de l'algorithme de Buch pour les tableaux à valeurs sur des ensembles et de l'algorithme de Worley et Sagan pour les tableaux décalés. Comme application, nous obtenons une formule de Pieri pour un analogue en K-théorie des Q-functions de Schur.

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