Characterization of Isometric Words based on Swap and Mismatch Distance

In this paper we consider an edit distance with swap and mismatch operations, called tilde-distance, and introduce the corresponding definition of tilde-isometric word. Isometric words are classically defined with respect to Hamming distance and combine the notion of edit distance with the property that a word does not appear as factor in other words. A word f is said tilde-isometric if, for any pair of f-free words u and v, there exists a minimal transformation from u to v via the related edit operations such that all the intermediate words are also f-free. This new setting is here studied giving a full characterization of the tilde-isometric words in terms of overlaps with errors.