2025/08/27 by Adamson, Duncan, Dudey, Moritz, Fleischmann, Pamela +1
#Combinatorics (math.CO) #Computation and Language (cs.CL) #FOS: Computer and information sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.2508.19619
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.