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arXiv · 1705.10277

Inverse Lyndon words and Inverse Lyndon factorizations of words

Paola Bonizzoni·Clelia De Felice·Rocco Zaccagnino·Rosalba Zizza
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Abstract

Motivated by applications to string processing, we introduce variants of the Lyndon factorization called inverse Lyndon factorizations. Their factors, named inverse Lyndon words, are in a class that strictly contains anti-Lyndon words, that is Lyndon words with respect to the inverse lexicographic order. The Lyndon factorization of a nonempty word w is unique but w may have several inverse Lyndon factorizations. We prove that any nonempty word w admits a canonical inverse Lyndon factorization, named ICFL(w), that maintains the main properties of the Lyndon factorization of w: it can be computed in linear time, it is uniquely determined, it preserves a compatibility property for sorting suffixes. In particular, the compatibility property of ICFL(w) is a consequence of another result: any factor in ICFL(w) is a concatenation of consecutive factors of the Lyndon factorization of w with respect to the inverse lexicographic order.

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Paola Bonizzoni, Clelia De Felice, Rocco Zaccagnino, Rosalba Zizza. 2017-12-17. Inverse Lyndon words and Inverse Lyndon factorizations of words. https://doi.org/10.1016/j.aam.2018.08.005

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