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Factorization of the Robinson-Schensted-Knuth correspondence. (English) Zbl 1059.05106
Summary: In [D. P. Little, Adv. Math. 174, 236–253 (2003; Zbl 1018.05102)], a bijection between collections of reduced factorizations of elements of the symmetric group was described. Initially, this bijection was used to show the Schur positivity of the Stanley symmetric functions. Further investigations have revealed that our bijection has strong connections to other more familiar combinatorial algorithms. In this paper we show how the Robinson-Schensted-Knuth correspondence can be decomposed into a sequence of applications of this bijection.

05E10 Combinatorial aspects of representation theory
Full Text: DOI
[1] Billey, S.C.; Jockusch, W.; Stanley, R.P., Some combinatorial properties of Schubert polynomials, J. algebraic combin., 2, 4, 345-374, (1993) · Zbl 0790.05093
[2] Knuth, D.E., Permutations, matrices, and generalized Young tableaux, Pacific J. math., 34, 709-727, (1970) · Zbl 0199.31901
[3] Lascoux, A.; Schützenberger, M.-P., Schubert polynomials and the littlewood – richardson rule, Lett. math. phys., 10, 2-3, 111-124, (1985) · Zbl 0586.20007
[4] Little, D.P., Combinatorial aspects of the lascoux – schützenberger tree, Adv. math., 174, 2, 236-253, (2003) · Zbl 1018.05102
[5] Schensted, C., Longest increasing and decreasing subsequences, Canad. J. math., 13, 179-191, (1961) · Zbl 0097.25202
[6] Stanley, R.P., On the number of reduced decompositions of elements of Coxeter groups, European J. combin., 5, 4, 359-372, (1984) · Zbl 0587.20002
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