On Special k-Spectra, k-Locality, and Collapsing Prefix Normal Words

How to reconstruct a word from a given set ofscattered factors? How to determine thelocalityof a word? Or how to determine theprefix normal words recursively? Combinatorics on words, even though this domain is relatively young, has by now a lot of subdomains, which all seek to deter-mine the secrets of various words that share a common pattern. Aiming for an understanding of this pattern or even find such apattern is often a challenging task. In Part I, scattered factors are investigated with respect to therecon-struction problemand thescattered factor universality. In Part II, thek-locality of repetitions of words and palindromes is determined. Finally, in Part III, a recursive approach to determine prefix normalforms is given.

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