The Skeleton of a Reduced Word and a Correspondence of Edelman and Greene

Stefan Felsner ()
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Stefan Felsner: Freie Universität Berlin, FB Mathematik und Informatik

A chapter in Formal Power Series and Algebraic Combinatorics, 2000, pp 179-190 from Springer

Abstract: Abstract Stanley conjectured that the number of maximal chains in the weak Bruhat order of S n , or equivalently the number of reduced decompositions of the reverse of the identity permutation revn = n, n − 1, n − 2,..., 2, 1, equals the number of standard Young tableaux of staircase shape s = {n − 1, n −2,...,1}. Originating from this conjecture remarkable connections between standard Young tableaux and reduced words have been discovered. Stanley proved his conjecture algebraicaly, later Edelman and Greene found a bijective proof. We provide a generalization of the Edelman and Greene bijection to a larger class of words. The proof is inspired by Viennot’s planarized proof of the Robinson-Schensted correspondence. As it is the case with the classical correspondence the planarized proofs have their own beauty and simplicity.

Keywords: Young Tableau; Maximal Chain; Cover Graph; Wiring Diagram; Standard Young Tableau (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-04166-6_16

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DOI: 10.1007/978-3-662-04166-6_16

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