The problem is described thus: Given a string of n different characters, choose a substring of length k and define a cyclic permutation on it. Take the k-cycle to another substring of length k by shifting it along the string. So if you have a string of length n and a pair of k-cycles, k < n, is there a way to predict how compositions of the pair acting on the string will behave? Can you predict the order of some composition, given you have only a pair of cyclic permutations and their inverses to play with? An example: if n is 5, five different characters might be: abcde. The pair of cycles in cycle notation might be (123) and (345). they intersect with the third character in the string. Already there are some obvious details. Given the above pair of cycles have inverses, there are four possible combinations, but I can multiply that by 2 to get the number of possible compositions. Is there a general formula that can tell me the order of each composition?