zbMATH — the first resource for mathematics

Dual equivalence with applications, including a conjecture of Proctor. (English) Zbl 0760.05093
The author establishes a bijection between standard tableaux of “shifted staircase” type and reduced expressions for the longest element in the Coxeter group. He also proves a conjecture of Stanley and determines the “dual Knuth relations” for the shifted Schensted correspondence.

05E10 Combinatorial aspects of representation theory
05E05 Symmetric functions and generalizations
20F55 Reflection and Coxeter groups (group-theoretic aspects)
Full Text: DOI
[1] Edelman, P.; Greene, C., Balanced tableaux, Adv. math., 63, 1, 42-99, (1987) · Zbl 0616.05005
[2] Haiman, M., On mixed insertion, symmetry, and shifted Young tableaux, J. combin. theory ser. A, 50, 2, 196-225, (1989) · Zbl 0697.05005
[3] Haiman, M.; Kim, D., A characterization of generalized staircases, Discrete math., 99, 115-122, (1992), (this Vol.) · Zbl 0760.05092
[4] Knuth, D.E., Permutations, matrices, and generalized Young tableaux, Pacific J. math., 34, 709-727, (1970) · Zbl 0199.31901
[5] W. Kraskiewicz, Reduced decompositions in hyperoctahedral groups, Manuscript, Mathematical Institute, Torun, Poland. · Zbl 0717.05005
[6] Lascoux, A.; Schützenberger, M.-P., Structure de Hopf de l’anneau de cohomologie et de l’anneau de Grothendieck d’une variete de drapeaux, C. R. acad. sci. Paris Sér. I math., 295, 629-633, (1982) · Zbl 0542.14030
[7] Sagan, B.E., Shifted tableaux, Schur Q-functions, and a conjecture of R. Stanley, J. combin. theory ser. A, 45, 1, 62-103, (1987) · Zbl 0661.05010
[8] Schützenberger, M.-P., Promotion des morphisms d’ensembles ordonnes, Discrete math., 2, 73-94, (1972) · Zbl 0279.06001
[9] Schützenberger, M.-P., La correspondance de Robinson, (), 59-113 · Zbl 0398.05011
[10] Stanley, R.P., On the number of reduced decompositions of elements of Coxeter groups, European J. combin., 5, 359-372, (1984) · Zbl 0587.20002
[11] R.P. Stanley, private communication.
[12] Worley, D.R., A theory of shifted Young tableaux, ()
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.