V-Words, Lyndon Words and Galois Words
<|reference_start|>V-Words, Lyndon Words and Galois Words: We say that a family $\mathcal{W}$ of strings over $\Sigma^+$ forms a Unique Maximal Factorization Family (UMFF) if and only if every $w \in \mathcal{W}$ has a unique maximal factorization. Further, an UMFF $\mathcal{W}$ is called a circ-UMFF whenever it contains exactly one rotation of every primitive string $x \in \Sigma^+$. $V$-order is a non-lexicographical total ordering on strings that determines a circ-UMFF. In this paper we propose a generalization of circ-UMFF called the substring circ-UMFF and extend combinatorial research on $V$-order by investigating connections to Lyndon words. Then we extend these concepts to any total order. Applications of this research arise in efficient text indexing, compression, and search problems.<|reference_end|>
@article{daykin2024v-words,,
    title={V-Words, Lyndon Words and Galois Words},
    author={Jacqueline W. Daykin, Neerja Mhaskar, and W. F. Smyth},
    journal={arXiv preprint arXiv:2409.02757},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.02757},
    primaryClass={cs.DS}
}