On Brlek-Reutenauer conjecture
Combinatorics
2013-02-05 v1
Abstract
Brlek and Reutenauer conjectured that any infinite word u with language closed under reversal satisfies the equality 2D(u)=\sum_{n=0}^{\infty} T(n) in which D(u) denotes the defect of u and T(n) denotes C(n+1)-C(n)+2-P(n+1)-P(n), where C and P are the factor and palindromic complexity of u, respectively. Brlek and Reutenauer verified their conjecture for periodic infinite words. We prove the conjecture for uniformly recurrent words. Moreover, we summarize results and some open problems related to defect, which may be useful for the proof of Brlek-Reutenauer Conjecture in full generality.
Cite
@article{arxiv.1101.5083,
title = {On Brlek-Reutenauer conjecture},
author = {Lubomira Balkova and Edita Pelantova and Stepan Starosta},
journal= {arXiv preprint arXiv:1101.5083},
year = {2013}
}