Abstract
We formulate and prove a defect theorem for bi-infinite words. Let X be a finite set of words over a finite alphabet. If a nonperiodic bi-infinite word w has two X-factorizations, then the combinatorial rank of X is at most card(X)−1 , i.e., there exists a set F such that X⊆F + with card(F)< card(X) . Moreover, in the case when the combinatorial rank of X equals card(X) , the number of periodic bi-infinite words which have two different X-factorizations is finite.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
