Balanced tableaux

Edelman, Paul H.; Greene, Casey S.

doi:10.1016/0001-8708(87)90063-6

Cited by 212 publications

(404 citation statements)

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“…For a general shape λ there seems to be no obvious pattern to the sizes of the orbits. However, for certain shapes, notably Haiman's "generalized staircases" more can be said [3] (see also Edelman and Greene [1,Cor. 7.23]).…”

Section: Remark 12mentioning

confidence: 99%

Promotion and cyclic sieving via webs

2008

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Section: Remark 12mentioning

confidence: 99%

Promotion and cyclic sieving via webs

2008

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“…Therefore, case (3) of the above bumping procedure is only applied when P i contains w i and w i + 1. This shows that the pair of Young tableaux associated to a reduced word ω by our construction is the same as the pair associated to ω by the generalized RSK correspondence of Edelman and Greene ( [2], Defin.6.21).…”

Section: Proofs Of Theorems 2 Andmentioning

confidence: 57%

“…12 switch [2,1] is bad, however, the right set of switches is very good. We are ready now to formulate our main results.…”

Section: Proposition 5 To Every Quasi-word ω Of Length R the Above Mmentioning

confidence: 99%

The Skeleton of a Reduced Word and a Correspondence of Edelman and Greene

Felsner

2000

Formal Power Series and Algebraic Combinatorics

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Stanley conjectured that the number of maximal chains in the weak Bruhat order of S n , or equivalently the number of reduced decompositions of the reverse of the identity permutation w 0 = n, n − 1, n − 2, . . . , 2, 1, equals the number of standard Young tableaux of staircase shape s = {n − 1, n − 2, . . . , 1}. Originating from this conjecture remarkable connections between standard Young tableaux and reduced words have been discovered. Stanley proved his conjecture algebraically, later Edelman and Greene found a bijective proof. We provide an extension of the Edelman and Greene bijection to a larger class of words. This extension is similar to the extension of the Robinson-Schensted correspondence to two line arrays. Our proof is inspired by Viennot's planarized proof of the Robinson-Schensted correspondence. As it is the case with the classical correspondence the planarized proofs have their own beauty and simplicity.

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“…(This construction is essentially equivalent to the construction of standard Young tableaux or, for instance, injective balanced labelings for permutation diagrams [1,2].) 3.2.…”

Section: Specht Modulesmentioning

confidence: 99%