Word Chain Generators for Prefix Normal Words
Combinatorics
2025-08-28 v1 Computation and Language
Abstract
In 2011, Fici and Lipt\'ak introduced prefix normal words. A binary word is prefix normal if it has no factor (substring) that contains more occurrences of the letter 1 than the prefix of the same length. Among the open problems regarding this topic are the enumeration of prefix normal words and efficient testing methods. We show a range of characteristics of prefix normal words. These include properties of factors that are responsible for a word not being prefix normal. With word chains and generators, we introduce new ways of relating words of the same length to each other.
Cite
@article{arxiv.2508.19619,
title = {Word Chain Generators for Prefix Normal Words},
author = {Duncan Adamson and Moritz Dudey and Pamela Fleischmann and Annika Huch},
journal= {arXiv preprint arXiv:2508.19619},
year = {2025}
}