Abstract
In this paper, first, we introduce two classification criteria of non-isometric words, and characterize every type of non-isometric words. Then, according to those characterizations, a family of words that 2-isometric but not 3-isometric is found, and the words with maximum and minimum index are characterized. Next, an O(|f|2) algorithm is designed, which is presented to compute the index of a non-isometric word and determine what class that a word belongs to. Finally, several problems are listed for further investigation.
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