On Infinite Prefix Normal Words
Abstract
Prefix normal words are binary words that have no factor with more s than the prefix of the same length. Finite prefix normal words were introduced in [Fici and Lipt\'ak, DLT 2011]. In this paper, we study infinite prefix normal words and explore their relationship to some known classes of infinite binary words. In particular, we establish a connection between prefix normal words and Sturmian words, between prefix normal words and abelian complexity, and between prefix normality and lexicographic order.
Cite
@article{arxiv.1811.06273,
title = {On Infinite Prefix Normal Words},
author = {Ferdinando Cicalese and Zsuzsanna Lipták and Massimiliano Rossi},
journal= {arXiv preprint arXiv:1811.06273},
year = {2021}
}
Comments
22 pages, 5 figures, 1 Table, accepted in Theoret. Comp. Sc.. This is the journal version of the paper with the same title at accepted at SOFSEM 2019 (45th International Conference on Current Trends in Theory and Practice of Computer Science, Nov\'y Smokovec, Slovakia, January 27-30, 2019)