Type B plactic relations for $r$-domino tableaux
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) (2009)
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The recent work of Bonnafé et al. (2007) 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 given two signed permutations have the same insertion $r$-domino tableaux in Garfinkle's algorithm (1990). 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 tool for their proofs.
@article{DMTCS_2009_special_256_a22,
author = {Ta\c{s}k{\i}n, M\"uge},
title = {Type {B} plactic relations for $r$-domino tableaux},
journal = {Discrete mathematics & theoretical computer science},
year = {2009},
volume = {DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)},
doi = {10.46298/dmtcs.2700},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2700/}
}
TY - JOUR AU - Taşkın, Müge TI - Type B plactic relations for $r$-domino tableaux JO - Discrete mathematics & theoretical computer science PY - 2009 VL - DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) UR - http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2700/ DO - 10.46298/dmtcs.2700 LA - en ID - DMTCS_2009_special_256_a22 ER -
%0 Journal Article %A Taşkın, Müge %T Type B plactic relations for $r$-domino tableaux %J Discrete mathematics & theoretical computer science %D 2009 %V DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) %U http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2700/ %R 10.46298/dmtcs.2700 %G en %F DMTCS_2009_special_256_a22
Taşkın, Müge. Type B plactic relations for $r$-domino tableaux. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) (2009). doi: 10.46298/dmtcs.2700
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