{"ID":2877502,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.19619","arxiv_id":"2508.19619","title":"Word Chain Generators for Prefix Normal Words","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.","short_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...","url_abs":"https://arxiv.org/abs/2508.19619","url_pdf":"https://arxiv.org/pdf/2508.19619v1","authors":"[\"Duncan Adamson\",\"Moritz Dudey\",\"Pamela Fleischmann\",\"Annika Huch\"]","published":"2025-08-27T06:56:45Z","proceeding":"math.CO","tasks":"[\"math.CO\",\"cs.CL\"]","methods":"[]","has_code":false}