Cycles, bicycles, tricycles and more
Barry Lewis · The Mathematical Gazette · 2005
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 }.