In mathematics and computer science, the critical exponent of a finite or infinite sequence of symbols over a finite alphabet describes the largest number of times a contiguous subsequence can be repeated.
For example, the critical exponent of "Mississippi" is 7/3, as it contains the string "ississi", which is of length 7 and period 3.
The word w is α-power-free if it contains no factors which are β-powers for any β ≥ α.
is a word (possibly infinite), then the critical exponent of
[4] The repetition threshold of an alphabet A of n letters is the minimum critical exponent of infinite words over A: clearly this value RT(n) depends only on n. For n=2, any binary word of length four has a factor of exponent 2, and since the critical exponent of the Thue–Morse sequence is 2, the repetition threshold for binary alphabets is RT(2) = 2.