Journal of the ACM (JACM)
Rotations of periodic strings and short superstrings
Journal of Algorithms
A fast string searching algorithm
Communications of the ACM
Theory of Codes
Reconstructing strings from substrings in rounds
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
A proof of the extended Duval's conjecture
Theoretical Computer Science - Combinatorics on words
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
On the Relation between Periodicity and Unbordered Factors of Finite Words
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
The Ehrenfeucht-Silberger Problem
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
The Ehrenfeucht-Silberger problem
Journal of Combinatorial Theory Series A
Automatic theorem-proving in combinatorics on words
CIAA'12 Proceedings of the 17th international conference on Implementation and Application of Automata
Linear computation of unbordered conjugate on unordered alphabet
Theoretical Computer Science
| Hi-index | 0.01 |
The relationship between the length of a word and the maximum length of its unbordered factors is investigated in this article. Consider a finite word w of length n. We call a word bordered if it has a proper prefix, which is also a suffix of that word. Let μ(w) denote the maximum length of all unbordered factors of w, and let ∂(w) denote the period of w. Clearly, μ(w) ≤ ∂(w). We establish that μ(w) = ∂(w), if w has an unbordered prefix of length μ(w) and n ≥ 2μ(w) − 1. This bound is tight and solves the stronger version of an old conjecture by Duval [1983]. It follows from this result that, in general, n ≥ 3μ(w) − 3 implies μ(w) = ∂(w), which gives an improved bound for the question raised by Ehrenfeucht and Silberger in 1979.