An inversion statistic for reduced words

We study the graph on reduced words with edges given by the Coxeter relations for the symmetric group. We define a statistic on reduced words for a given permutation, analogous to Coxeter length for permutations, for which the graph becomes ranked with unique maximal element. We show this statistic...

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Bibliographic Details
Published in:Advances in applied mathematics 2019-06, Vol.107, p.1-21
Main Author: Assaf, Sami
Format: Article
Language:English
Subjects:
Balanced tableaux
Inversion
Reduced words
Yang–Baxter moves
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Summary:We study the graph on reduced words with edges given by the Coxeter relations for the symmetric group. We define a statistic on reduced words for a given permutation, analogous to Coxeter length for permutations, for which the graph becomes ranked with unique maximal element. We show this statistic extends naturally to balanced labellings, and use it to recover enumerative results of Edelman and Greene and of Reiner and Roichman.
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2019.02.005