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

Authors: Cho, Soojin and Park, Kyoungsuk

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 $B$.

Source : oai: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
Submitted 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]