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A short hook-lengths bijection inspired by the Greene-Nijenhuis-Wilf proof

✍ Scribed by Doron Zeilberger


Publisher
Elsevier Science
Year
1984
Tongue
English
Weight
930 KB
Volume
51
Category
Article
ISSN
0012-365X

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✦ Synopsis


The cdebruted ri-we-Rdinson-ThraU (Canad. J. Math. 6 (1954) 316-324) hook-lengths formula, counting the foung tableaux of a specified shape, is given a shart bijective proof. This proof was obtained by translating the elegant Greene-Nijenhuis-Wilf proof (Adv. in Math. 31 (1979) f&l-109) into bijective language. 0. Gettbg baked AYoungtableauofsha~A=(h,,...,A,),h,~A,~~==~A,>O,isanarray (dj: 'IGiSWi, 1 GjG&) satisfying qj <*+lj and ej C= Rj+l (whenever applicable) such that every integer between 1 and n( = AI + l l l + A,,,) appears exactly once among its II entries. For example 12 4 3 6 10 5 7 8 9