Proof of a conjecture on multisets of hook numbers

1997 ◽  
Vol 1 (1) ◽  
pp. 391-394 ◽  
Author(s):  
Amitai Regev ◽  
Doron Zeilberger
Keyword(s):  
Hook Numbers

scholarly journals Asymptotics of Young Diagrams and Hook Numbers

10.37236/1307 ◽  
1997 ◽  
Vol 4 (1) ◽  
Author(s):  
Amitai Regev ◽  
Anatoly Vershik
Keyword(s):  
Asymptotic Theory ◽  
Asymptotic Methods ◽  
Symmetric Groups ◽  
Schur Functions ◽  
Young Diagrams ◽  
Arithmetic Properties ◽  
Hook Formula ◽  
Hook Numbers

Asymptotic calculations are applied to study the degrees of certain sequences of characters of symmetric groups. Starting with a given partition $\mu$, we deduce several skew diagrams which are related to $\mu$. To each such skew diagram there corresponds the product of its hook numbers. By asymptotic methods we obtain some unexpected arithmetic properties between these products. The authors do not know "finite", nonasymptotic proofs of these results. The problem appeared in the study of the hook formula for various kinds of Young diagrams. The proofs are based on properties of shifted Schur functions, due to Okounkov and Olshanski. The theory of these functions arose from the asymptotic theory of Vershik and Kerov of the representations of the symmetric groups.

scholarly journals Hook and shifted hook numbers

1990 ◽  
Vol 79 (2) ◽  
pp. 153-167
Author(s):  
R.M. Grassl ◽  
A.P. Mullhaupt
Keyword(s):  
Hook Numbers

scholarly journals Dyck paths and a bijection for multisets of hook numbers

2002 ◽  
Vol 254 (1-3) ◽  
pp. 153-164 ◽  
Author(s):  
Ian Goulden ◽  
Alexander Yong
Keyword(s):  
Dyck Paths ◽  
Hook Numbers
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