Ostrowski numeration and repetitions in words

Abstract: One of the classical results in combinatorics on words is Dejean's Theorem, which specifies the smallest exponent of repetitions that are avoidable on a given alphabet. One can ask if it is possible to determine this quantity (called the *repetition threshold*) for certain families of infinite words. For example, it is known that the repetition threshold for Sturmian words is 2+phi, and this value is reached by the Fibonacci word. Recently, this problem has been studied for *balanced words* (which generalize Sturmian words) and *rich words*. The infinite words constructed to resolve this problem can be defined in terms of the Ostrowski-numeration system for certain continued-fraction expansions. They can be viewed as *Ostrowski-automatic* sequences, where we generalize the notion of *k-automatic sequence* from the base-k numeration system to the Ostrowski numeration system.

dynamical systemsnumber theory

Audience: researchers in the topic

One World Numeration seminar

Series comments: Description: Online seminar on numeration systems and related topics

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