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A short Hook-lengths bijection inspired by the Greene-Nijenhuis-Wilf proof. (English) Zbl 0551.05010

This is a bijective proof of the Frame-Robinson-Thrall hook-lengths formula [see J. S. Frame, G. de B. Robinson and R. M. Thrall, Can. J. Math. 6, 316-324 (1954; Zbl 0055.254)] for counting Young tableaux of a specified shape.
Reviewer: D.Bressoud

MSC:

05A15 Exact enumeration problems, generating functions

Citations:

Zbl 0055.254
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References:

[1] Frame, J. S.; Robinson, G. D.; Thrall, R. M., The hook graphs of the symmetric group, Canadian J. Math., 6, 316-324 (1954) · Zbl 0055.25404
[2] D. Franzblau and D. Zeilberger, A bijection proof of the hook-lengths formula, J. Algorithms.; D. Franzblau and D. Zeilberger, A bijection proof of the hook-lengths formula, J. Algorithms. · Zbl 0498.68042
[3] Garsia, A. M.; Milne, S. C., A Rogers-Ramanujan bijection, J. Combin. Theory Ser. A, 31, 289-339 (1981) · Zbl 0477.05009
[4] Greene, C.; Nijenhuis, A.; Wilf, H. S., A probabilistic proof of a formula for the number of Young tableaux of a given shape, Adv. in Math., 31, 104-109 (1979) · Zbl 0398.05008
[5] Knuth, D. E., The Art of Computer Programming, (Sorting and Searching, Vol. 3 (1973), Addison-Wesley: Addison-Wesley Reading, MA) · Zbl 0191.17903
[6] J.B. Remmel, Bijective proofs of some classical partition identities, J. Combin. Theory, in press.; J.B. Remmel, Bijective proofs of some classical partition identities, J. Combin. Theory, in press. · Zbl 0491.05012
[7] J.B. Remmel, Bijective proofs of formulae for the number of standard Young tableaux, UCSD preprint.; J.B. Remmel, Bijective proofs of formulae for the number of standard Young tableaux, UCSD preprint.
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