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The hook-length formula and generalised Catalan numbers

Published online by Cambridge University Press:  23 January 2015

Martin Griffiths  and
Nick Lord
Martin Griffiths
Affiliation:
School of Education, University of Manchester, Oxford Road, Manchester M13 9PL, e-mail:gazette-reviews@m-a.org.uk
Nick Lord
Affiliation:
Tonbridge School, Kent TN9 1JP
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Extract

In [1] there is a rather nice story regarding the coming into being of the hook-length formula. The year was 1953, and the Canadian mathematician Gilbert Robinson was visiting a fellow mathematician, James Frame, at Michigan State University. One of their discussions concerned the work of Ralph Staal [2], an ex-student of Robinson, and this led to Frame conjecturing the formula. Apparently, Robinson was not at all convinced initially that the formula could be as simple as the one Frame was proposing. He was, however, eventually won over, and the combined efforts of these two mathematicians soon elicited a proof.

Type
Articles
Information
The Mathematical Gazette , Volume 95 , Issue 532 , March 2011 , pp. 23 - 30
Copyright
Copyright © The Mathematical Association 2011

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References

1. Sagan, B. E., The symmetric group: representions, combinatorial algorithms & symmetric functions, Wadsworth & Brooks/Cole (1991).Google Scholar
2. Staal, R. A., Star diagrams and the symmetric group, Canadian Journal of Mathematics 2 (1950) pp. 79–92.Google Scholar
3. Frame, J. S., de B. Robinson, G. and Thrall, R. M., The hook graphs of the symmetric group, Canadian Journal of Mathematics 6 (1954) pp.316–325.CrossRefGoogle Scholar
4. Griffiths, M., The backbone of Pascal's triangle, United Kingdom Mathematics Trust (2008).Google Scholar
5. Novelli, J., Pak, I. and Stoyanovskii, A. V., A direct bijective proof of the hook-length formula, Discrete Mathematics and Theoretical Computer Science 1 (1997) pp. 53–67. http://www.emis.de/joumals/DMTCS/volumes/abstracts/pdfpapers/\\dm010104.pdf Google Scholar
6. Bandlow, J., An elementary proof of the hook formula, The Electronic Journal of Combinatorics 15 (2008). http://www.math.upenn.edu/~jbandlow/papers/hookFormula.pdf Google Scholar
7. Parmer, Julian, The school photo problem, Mathematics in School 37.4 (September 2008) pp. 31–33.Google Scholar
8. Sloane, N.J. A., The On-line encyclopedia of integer sequences. http://www.research.att.com/~njas/sequences/ Google Scholar
9. Griffiths, M., ‘Catch-up’ numbers, Math. Gaz. 91 (November 2007) pp. 500–509.CrossRefGoogle Scholar