Characterization of Isometric Words based on Swap and Mismatch Distance

TL;DR

This paper introduces the concept of tilde-isometric words based on a new edit distance with swap and mismatch operations, providing a full characterization of these words through overlaps with errors.

Contribution

It defines tilde-isometric words using a novel edit distance and characterizes them in terms of overlaps with errors, extending classical isometric word theory.

Findings

Full characterization of tilde-isometric words.

Connection between tilde-isometric words and overlaps with errors.

Extension of classical isometric word concepts.

Abstract

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 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.