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arXiv · 2508.19619

Word Chain Generators for Prefix Normal Words

Duncan Adamson·Moritz Dudey·Pamela Fleischmann·Annika Huch
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Abstract

In 2011, Fici and Lipták 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.

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Duncan Adamson, Moritz Dudey, Pamela Fleischmann, Annika Huch. 2025-08-27. Word Chain Generators for Prefix Normal Words. https://arxiv.org/abs/2508.19619

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