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Uspekhi Mat. Nauk, 2005, Volume 60, Issue 2(362), Pages 79–142 (Mi umn1402)  

This article is cited in 4 scientific papers (total in 4 papers)

Arrays and the combinatorics of Young tableaux

V. I. Danilov, G. A. Koshevoy

Central Economics and Mathematics Institute, RAS

Abstract: The classical theory of Young tableaux is presented in the rather new and non-traditional language of arrays. With the usual operations (or algorithms) of insertion and jeu de taquin as a starting point, more elementary operations on arrays are introduced. The set of arrays equipped with these operations forms an object which can be referred to as a bicrystal. This formalism is presented in the first part of the paper, and its exposition is based on the theorem that the vertical and horizontal operators commute. In the second part the apparatus of arrays is used to present some topics in the theory of Young tableaux, namely, the plactic monoid, Littlewood–Richardson rule, Robinson–Schensted–Knuth correspondence, dual tableaux, plane partitions, and so on.

DOI: https://doi.org/10.4213/rm1402

Full text: PDF file (705 kB)
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English version:
Russian Mathematical Surveys, 2005, 60:2, 269–334

Bibliographic databases:

UDC: 519.116+519.142.1
MSC: Primary 05E05; Secondary 05B30, 05E05
Received: 14.07.2004

Citation: V. I. Danilov, G. A. Koshevoy, “Arrays and the combinatorics of Young tableaux”, Uspekhi Mat. Nauk, 60:2(362) (2005), 79–142; Russian Math. Surveys, 60:2 (2005), 269–334

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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. V. I. Danilov, G. A. Koshevoy, “The Robinson–Schensted–Knuth correspondence and the bijections of commutativity and associativity”, Izv. Math., 72:4 (2008), 689–716  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Pak I., Vallejo E., “Reductions of Young tableau bijections”, SIAM J. Discrete Math., 24:1 (2010), 113–145  crossref  mathscinet  zmath  isi  elib
    3. Farber M., Hopkins S., Trongsiriwat W., “Interlacing Networks: Birational Rsk, the Octahedron Recurrence, and Schur Function Identities”, 133, 2015, 339–371  crossref  mathscinet  zmath  isi
    4. Patrick Doolan, Sangjib Kim, “The Littlewood-Richardson rule and Gelfand-Tsetlin patterns”, Algebra Discrete Math., 22:1 (2016), 21–47  mathnet  mathscinet
  • Успехи математических наук Russian Mathematical Surveys
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