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On Hooks of Skew Young Diagrams and Bars in Shifted Diagrams
Christine Bessenrodt
Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg, D-39016 Magdeburg, Germany
bessen@mathematik.uni-magdeburg.de
Annals of Combinatorics 5(1) p.37-49 March, 2001
AMS Subject Classification: 05Exx, 05A17
Abstract:
Illustrating the effectiveness of the methods introduced in [1] we investigate here hooks in skew Young diagrams and bars in shifted diagrams; this is partially motivated by recent work by Regev. In particular, we provide short combinatorial proofs for refined identities on multisets of hooks in the cases of shift-symmetric partitions.
Keywords: skew Young diagrams, hooks, shifted diagrams, bars

References:

1.  C. Bessenrodt, On hooks of Young diagrams. Annals of Combin. 2 (1998) 103–110.

2.  I.G. Macdonald, Symmetric Functions and Hall Polynomials, Oxford University Press, 2nd Edition, 1995.

3.  J.B. Olsson, Combinatorics and representations of finite groups. Vorlesungen aus dem Fachbereich Mathematik der Universität GH Essen, Heft 20, 1993.

4.  A. Regev and A. Vershik, Asymptotics of Young diagrams and hook numbers. Electr. J. Combin. 4 (1997) #R22, 12pp.

5.  A. Regev, Generalized hook and content numbers identities, preprint, (1999).

6.  A. Regev, Generalized hook and content numbers identities - the projective case, preprint, (1999).