论文信息 - La correspondance de Robinson-Schensted pour les tableaux oscillants gauches

La correspondance de Robinson-Schensted pour les tableaux oscillants gauches

We introduce an analog of the Robinson Schensted algorithm for skew oscillating tableaux which generalizes the well-known correspondence for standard tableaux. We show that this new algorithm enjoys some of the same properties as the original. In particular, it is still true that replacing a permutation by its inverse exchanges the two output tableaux. These facts permit us to derive a number of identities involving the number of such tableaux.

Bruce E. Sagan | Serge Dulucq | Serge Dulucq | Bruce E. Sagan

[1] Lucile Favreau. Combinatoire des tableaux oscillants et des polynomes de Bessel , 1991 .

[2] Tom Roby,et al. Applications and extensions of Fomin's generalization of the Robinson-Schensted correspondence to differential posets , 1991 .

[3] Bruce E. Sagan,et al. The symmetric group - representations, combinatorial algorithms, and symmetric functions , 2001, Wadsworth & Brooks / Cole mathematics series.

[4] Sheila Sundaram. On the combinatorics of representations of Sp(2n,C) , 1986 .

[5] Serge Dulucq,et al. An analogue to Robinson-Schensted correspondence for oscillating tableaux. , 1988 .

[6] Sergey Fomin,et al. Schensted Algorithms for Dual Graded Graphs , 1995 .

[7] C. Schensted. Longest Increasing and Decreasing Subsequences , 1961, Canadian Journal of Mathematics.

[8] Alfred Young. On Quantitative Substitutional Analysis , 1928 .

[9] Bruce E. Sagan. Shifted tableaux, schur Q-functions, and a conjecture of R. Stanley , 1987, J. Comb. Theory, Ser. A.

[10] Marcel P. Schützenberger. Quelques remarques sur une Construction de Schensted. , 1963 .

[11] Bruce E. Sagan,et al. Robinson-schensted algorithms for skew tableaux , 1990, J. Comb. Theory A.

[12] Donald E. Knuth,et al. PERMUTATIONS, MATRICES, AND GENERALIZED YOUNG TABLEAUX , 1970 .

[13] Dale Raymond Worley,et al. A theory of shifted Young tableaux , 1984 .