✦ LIBER ✦
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
No coin nor oath required. For personal study only.
✦ 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