Soojin Cho ; Kyoungsuk Park - Alignments, crossings, cycles, inversions, and weak Bruhat order in permutation tableaux of type $B$

dmtcs:2484 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) - https://doi.org/10.46298/dmtcs.2484
Alignments, crossings, cycles, inversions, and weak Bruhat order in permutation tableaux of type $B$Article

Authors: Soojin Cho 1; Kyoungsuk Park 1

  • 1 Department of Mathematics [Ajou]

Alignments, crossings and inversions of signed permutations are realized in the corresponding permutation tableaux of type $B$, and the cycles of signed permutations are understood in the corresponding bare tableaux of type $B$. We find the relation between the number of alignments, crossings and other statistics of signed permutations, and also characterize the covering relation in weak Bruhat order on Coxeter system of type $B$ in terms of permutation tableaux of type $B$.

https://doi.org/10.46298/dmtcs.2484
Source: HAL:hal-01337820v1
Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Imported on: November 21, 2016
Keywords: crossing,inversion,Bruhat order,alignment,permutation tableaux of type $B$,Coxeter group of type $B$,signed permutation,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Licence: Attribution 4.0 International (CC BY 4.0)

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