@article{
    CzCKS11,
    author = "Czeizler, Elena and Czeizler, Eugen and Kari, Lila and Seki, Shinnosuke",
    note = "",
    responsibleauthor = "Czeizler, Eugen",
    language = "eng",
    title = {An extension of the Lyndon-Sch{\"u}tzenberger result to pseudoperiodic words},
    url = "http://dx.doi.org/10.1016/j.ic.2011.01.001",
    journal = "Information and computation",
    corerank = "B",
    number = "4",
    abstract = {One of the particularities of information encoded as DNA strands is that a string u contains basically the same information as its Watson–Crick complement, denoted here as $\theta(u)$. Thus, any expression consisting of repetitions of $u$ and $\theta(u)$ can be considered in some sense periodic. In this paper, we give a generalization of Lyndon and Sch\"{u}tzenberger’s classical result about equations of the form $u^l=v^nw^m$, to cases where both sides involve repetitions of words as well as their complements. Our main results show that, for such extended equations, if $l\geq5,n,m\geq3$, then all three words involved can be expressed in terms of a common word $t$ and its complement $\theta(t)$. Moreover, if $l\geq5$, then $n=m=3$ is an optimal bound. These results are established based on a complete characterization of all possible overlaps between two expressions that involve only some word $u$ and its complement $\theta(u)$, which is also obtained in this paper.},
    volume = "209",
    internalpdf = "genls.pdf",
    flags = "copy",
    il = "yes",
    year = "2011",
    keywords = {Pseudoperiodic word; (extended) Lyndon–Sch\"{u}tzenberger equation; Pseudo-primitive word; Antimorphic involution; Non-trivial overlap},
    unitcode = "",
    impactfactor = "A1",
    pages = "717--730"
}