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math.CO2024
Additive word complexity and Walnut
Pierre Popoli, Jeffrey Shallit, Manon Stipulanti
In combinatorics on words, a classical topic of study is the number of specific patterns appearing in infinite sequences. For instance, many works have been dedicated to studying t…
math.CO2024
The Repetition Threshold for Rote Sequences
Nicolas Ollinger, Jeffrey Shallit
We consider Rote words, which are infinite binary words with factor complexity . We prove that the repetition threshold for this class is . Our technique is purely computa…
math.CO2024
The reflection complexity of sequences over finite alphabets
Jean-Paul Allouche, John M. Campbell, Shuo Li +2
In combinatorics on words, the well-studied factor complexity function $ρ_{\infw{x}}$ of a sequence $\infw{x}$ over a finite alphabet counts, for every nonnegative integer , the…