Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-14T07:28:24.887Z Has data issue: false hasContentIssue false

Cycles, bicycles, tricycles and more

Published online by Cambridge University Press:  01 August 2016

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

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
Copyright
Copyright © The Mathematical Association 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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. 3945.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