Titlebook: Combinatorics on Words; 14th International C Anna Frid,Robert Merca? Conference proceedings 2023 The Editor(s) (if applicable) and The Auth

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978-3-031-33179-4The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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Minimal Complexities for?Infinite Words Written with?, LettersIn this extended abstract, we discuss the minimal subword complexity and the minimal abelian complexity functions for infinite .-ary words. This leads us to answer a question of Rauzy from 1983: cubic billiard words are a good generalization of Sturmian words for the abelian complexity.

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On the?Number of?Distinct Squares in?Finite Sequences: Some Old and?New Resultsed by Fraenkel and Simpson in 1998. They proved that the number of distinct squares, denoted as ., in a finite word . of length . is upper bounded by 2. and conjectured that . is no larger than .. In this note, we review some old and new findings concerning the square-counting problem and prove that ..

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