Séminaire Lotharingien de Combinatoire, 80B.79 (2018), 12 pp.
Svante Linusson and Samu Potka
Properties of the Edelman-Greene Bijection
Abstract.
Edelman and Greene constructed a bijective correspondence between the
reduced words of the reverse permutation in the symmetric group Sn
and standard Young tableaux of the staircase shape (n-1, n-2, ...,
1). Our motivation originates from random sorting networks, a line of
research initiated by Angel, Holroyd, Romik and Virág. We
reformulate one of their conjectures on the shapes of intermediate
configurations coming from random sorting networks. Properties of the
Edelman-Greene bijection restricted to 132-avoiding and 2143-avoiding
permutations are presented. We also consider the Edelman-Greene
bijection applied to non-reduced words.
Received: November 14, 2017.
Accepted: February 17, 2018.
Final version: April 1, 2018.
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