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Cycles, bicycles, tricycles and more

Published online by Cambridge University Press:  01 August 2016

Barry Lewis
Barry Lewis*
Affiliation:
21 Muswell Hill Road, London N10 3JB
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Extract

I wanted to call this article, Counting permutations that contain a specified number of cycles of a given length but the Editor pointed out the problems this might cause the Production Editor - it simply wouldn't fit the running head. Hence the chosen title and the subject matter. There is a very well known result, nonetheless startling, about the relative frequency of derangements amongst the permutations of [r] = {1,2,3,… , r }.

Type
Articles
Information
The Mathematical Gazette , Volume 89 , Issue 516 , November 2005 , pp. 392 - 402
Copyright
Copyright © The Mathematical Association 2004

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References

1. Goodstein, R. L., How unlikely, Math. Gaz. 23 (May 1939) p. 205.Google Scholar
2. Piggott, H. E., A question of hats, Math. Gaz. 33 (October 1949) p. 214.Google Scholar
3. Bizely, M. T. L., A note on derangements, Math. Gaz. 51 (May 1967) p. 118.Google Scholar
4. Dennett, J. R., Cricket and derangements, Math. Gaz 74 (March 1990) p. 2.Google Scholar
5. Wilf, Herbert; Generatingfunctionology, Academic Press (1994). Also available (for free!) from http://www.cis.upenn.edu/~wilf; pp. 39–45.Google Scholar
6. Remmel, J. B., Eur J Combinatorics 4 (1983) p. 371.Google Scholar
7. Dörrie, Heinrich, 100 Great Problems of Elementary Mathematics, Dover (1965) p. 19.Google Scholar
8. David, K., Rencontres Reencountered, Coll. Math. Journal 19 (1988) MAA, p. 139.Google Scholar