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Izv. RAN. Ser. Mat., 2008, Volume 72, Issue 4, Pages 67–96 (Mi izv708)  

This article is cited in 1 scientific paper (total in 1 paper)

The Robinson–Schensted–Knuth correspondence and the bijections of commutativity and associativity

V. I. Danilov, G. A. Koshevoy

Central Economics and Mathematics Institute, RAS

Abstract: The bijections of associativity and commutativity arise from symmetries of the Littlewood–Richardson coefficients. We define these bijections in terms of arrays and show that they coincide with analogous bijections defined in terms of discretely concave functions using the octahedron recurrence as well as with bijections defined in terms of Young tableaux. The main ingredient in the proof of their coincidence is a functional version of the Robinson–Schensted–Knuth correspondence.

DOI: https://doi.org/10.4213/im708

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English version:
Izvestiya: Mathematics, 2008, 72:4, 689–716

Bibliographic databases:

UDC: 512.815.1
MSC: 05E10, 52C07, 26B25
Received: 01.04.2005
Revised: 15.05.2007

Citation: V. I. Danilov, G. A. Koshevoy, “The Robinson–Schensted–Knuth correspondence and the bijections of commutativity and associativity”, Izv. RAN. Ser. Mat., 72:4 (2008), 67–96; Izv. Math., 72:4 (2008), 689–716

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Pak I., Vallejo E., “Reductions of Young tableau bijections”, SIAM J. Discrete Math., 24:1 (2010), 113–145  crossref  mathscinet  zmath  isi  elib  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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