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On mixed insertion, symmetry, and shifted Young tableaux. (English) Zbl 0697.05005
The author generalizes Schensted insertion to mixed insertion and uses the results to answer a number of questions about the Hall-Littlewood symmetric functions. A complete statement of results would be very long and very technical.
Reviewer: R.G.Stanton

05A10 Factorials, binomial coefficients, combinatorial functions
Full Text: DOI
[1] Greene, C, An extension of Schensted’s theorem, Adv. in math., 14, 254-265, (1974) · Zbl 0303.05006
[2] Knuth, D.E, Permutations, matrices, and generalized Young tableaux, Pacific J. math., 34, 709-727, (1970) · Zbl 0199.31901
[3] Macdonald, I.G, Symmetric functions and Hall polynomials, (1979), Oxford Univ. Press London/New York · Zbl 0487.20007
[4] Morris, A.O, A survey on Hall-Littlewood functions and their applications to representation theory, (), 136-154
[5] Sagan, B.E, Shifted tableaux, Schur \(Q\)-functions, and a conjecture of R. Stanley, J. combin. theory ser. A, 45, 62-103, (1987) · Zbl 0661.05010
[6] Schensted, C, Longest increasing and decreasing subsequences, Canad. J. math., 13, 179-191, (1961) · Zbl 0097.25202
[7] Sch├╝tzenberger, M.-P, La correspondance de Robinson, (), 59-113 · Zbl 0398.05011
[8] Stanley, R, Theory and application of plane partitions: part I, Stud. appl. math., 50, 2, 167-188, (1971) · Zbl 0225.05011
[9] Thomas, G.P, On Schensted’s construction and the multiplication of Schur functions, Adv. in math., 30, 8-32, (1978) · Zbl 0408.05004
[10] Worley, D.R, A theory of shifted Young tableaux, Ph.D. thesis MIT, (1984)
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