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Annals of Combinatorics

, Volume 2, Issue 2, pp 103–110 | Cite as

On hooks of Young diagrams

  • Christine Bessenrodt
Article

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].

AMS Subject Classification

05A17 05Exx 

Keywords

Young diagrams hooks hook numbers partitions Regev-Vershik-Conjecture 

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References

  1. 1.
    S. Janson, Hook lengths in a skew Young diagram. Electronic J. Combin.4 (1997) #R24, 5pp.Google Scholar
  2. 2.
    J. B. Olsson, Combinatorics and representations of finite groups, Vorlesungen aus dem Fachbereich Mathematik der Universität GH Essen, Heft 20, 1993Google Scholar
  3. 3.
    A. Regev and A. Vershik, Asymptotics of Young diagrams and hook numbers, Electronic J. Combin.4 (1997) #R22, 12pp.Google Scholar
  4. 4.
    A. Regev and D. Zeilberger, Proof of a conjecture on multisets of hook numbers, Ann. Combin.1 (4) (1997) 391–394.Google Scholar

Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Christine Bessenrodt
    • 1
  1. 1.Fakultät für MathematikOtto-von-Guericke-Universität MagdeburgMagdeburgGermany

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