Abstract
We present several properties of the complexity function of finite words, the function counting the number of different factors in a word, for each length. To establish a first set of properties, we use the de Bruijn graphs and the suffix tree representations of a word. This allows us to show some inequalities that control the variation as well as the maximal value of the complexity function. Motivated by the applications, we discuss the change of the complexity function when sliding or increasing the size of a window laid down on a sequence to be analysed.
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