On Defect Eeect of Bi-innnite Words
نویسنده
چکیده
We prove the following two variants of the defect theorem. Let X be a nite set of words over a nite alphabet. Then if a nonperiodic bi-in nite 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). Further, if card(X) = 2 and a bi-in nite word possesses two X-factorizations which are not shift-equivalent, then the primitive roots of the words in X are conjugates. Moreover, in the case card(F ) = card(X), the number of periodic bi-in nite words which have two di erent X-factorizations is nite and in the two-element case there is at most one such bi-in nite word. TUCS Research Group Mathematical Structures of Computer Science
منابع مشابه
Multiple factorizations of words and defect effect
We prove that if X is a nite preex set and w is a non-periodic bi-innnite word possessing 3 disjoint X-factorizations, then the combinatorial rank of X is at most card(X)?2. This is one of the rare cases when a cumulative defect eeect is known to hold. Finally, connections to the critical factorization theorem are discussed.
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