Geodesic
A symmetry property for $q$-weighted Robinson-Schensted and other branching insertion algorithms
Journal of Algebraic Combinatorics, Tome 40 (2014) no. 3, pp. 743-770.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

In [N. O'Connell and Y. Pei, Electron. J. Probab. 18, Paper No. 95, 25 p. (2013; Zbl 1278.05243)], a $q$-weighted version of the Robinson-Schensted algorithm was introduced. In this paper, we show that this algorithm has a symmetry property analogous to the well-known symmetry property of the usual Robinson-Schensted algorithm. The proof uses a generalisation of the growth diagram approach introduced by S. Fomin [J. Sov. Math. 41, No. 2, 979--991 (1988); translation from Zap. Nauchn. Semin. Leningrad. Otd. Mat. Inst. Steklova 155, 156--175 (1986; Zbl 0698.05003); J. Algebr. Comb. 3, No. 4, 357--404 (1994; Zbl 0810.05005); J. Algebr. Comb. 4, No. 1, 5--45 (1995; Zbl 0817.05077)]. This approach, which uses `growth graphs', can also be applied to a wider class of insertion algorithms which have a branching structure, including some of the other $q$-weighted versions of the Robinson-Schensted algorithm which have recently been introduced by A. Borodin and L. Petrov ["Nearest neighbor Markov dynamics on Macdonald processes", Preprint, arXiv:1305.5501].
Classification : 05A30, 05A05, 05C20, 05C85, 05E10, 05E05
Keywords: Robinson-Schensted algorithm, growth diagram, $q$-analogue, permutation 
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     title = {A symmetry property for $q$-weighted {Robinson-Schensted} and other branching insertion algorithms},
     journal = {Journal of Algebraic Combinatorics},
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Pei, Yuchen. A symmetry property for $q$-weighted Robinson-Schensted and other branching insertion algorithms. Journal of Algebraic Combinatorics, Tome 40 (2014) no. 3, pp. 743-770. http://geodesic.mathdoc.fr/item/JAC_2014__40_3_a6/