In mathematics, a sesquipower or Zimin word is a string over an alphabet with identical prefix and suffix.
Sesquipowers are unavoidable patterns, in the sense that all sufficiently long strings contain one.
Formally, let A be an alphabet and A∗ be the free monoid of finite strings over A.
The degree of a word w is thus the length of the longest bi-ideal sequence ending in w.[2] For a finite alphabet A on k letters, there is an integer M depending on k and n, such that any word of length M has a factor which is a sesquipower of order at least n. We express this by saying that the sesquipowers are unavoidable patterns.
[7] Fix a finite alphabet A and assume a total order on the letters.