Abstract
The well-known fact that there is always one more addable than removable box for a Young diagram is generalized to arbitrary hooks. As an application, this immediately implies a simple proof of a conjecture of Regev and Vershik [3] for which inductive proofs have recently been given by Regev and Zeilberger [4] and Janson [1].
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References
S. Janson, Hook lengths in a skew Young diagram. Electronic J. Combin.4 (1997) #R24, 5pp.
J. B. Olsson, Combinatorics and representations of finite groups, Vorlesungen aus dem Fachbereich Mathematik der Universität GH Essen, Heft 20, 1993
A. Regev and A. Vershik, Asymptotics of Young diagrams and hook numbers, Electronic J. Combin.4 (1997) #R22, 12pp.
A. Regev and D. Zeilberger, Proof of a conjecture on multisets of hook numbers, Ann. Combin.1 (4) (1997) 391–394.
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Bessenrodt, C. On hooks of Young diagrams. Annals of Combinatorics 2, 103–110 (1998). https://doi.org/10.1007/BF01608481
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DOI: https://doi.org/10.1007/BF01608481