Attractors of sequences coding beta-integers

Abstract: String attractor is an intensively studied object in Combinatorics on Words. In our talk, we will recall known results and also some previously used techniques. We will then describe minimal string attractors of prefixes of simple Parry sequences. These sequences form a coding of distances between consecutive beta-integers in numeration systems with a real base beta. Simple Parry sequences have been recently studied from this point of view and (not necessarily minimal) attractors of their prefixes have been described and a conjecture that attractors of alphabet size should be sufficient was stated. We prove this conjecture. Moreover, we provide attractors of prefixes of some particular form of binary non-simple Parry sequences.

formal languages and automata theorycombinatoricsdynamical systems

Audience: researchers in the topic

One World Combinatorics on Words Seminar

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