Bumping algorithm for set-valued shifted tableaux

• 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

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.