Permutation statistics and weak {B}ruhat order in permutation tableaux of type \(B\)

Permutation statistics and weak {B}ruhat order in permutation tableaux of type \(B\)

Many important statistics of signed permutations are realized in the corresponding permutation tableaux or bare tableaux of type \(B\): Alignments, crossings and inversions of signed permutations are realized in the corresponding permutation tableaux of type \(B\), and the cycles of signed permutati...

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Veröffentlicht in:arXiv.org 2014-12
Hauptverfasser: Cho, Soojin, Park, Kyoungsuk
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Inversions
Permutations
Statistics
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description Many important statistics of signed permutations are realized in the corresponding permutation tableaux or bare tableaux of type \(B\): 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 \(B\). This leads us to relate the number of alignments and crossings with other statistics of signed permutations and also to characterize the covering relation in weak Bruhat order on Coxeter system of type \(B\) in terms of permutation tableaux of type \(B\).
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subjects Inversions
Permutations
Statistics
title Permutation statistics and weak {B}ruhat order in permutation tableaux of type \(B\)
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