Well distributed occurrences property in infinite words – INSTITUT DE MATHÉMATIQUES DE MARSEILLE

Svetlana Puzynina
St Petersburg University, Russia
https://users.math-cs.spbu.ru/~puzynina/

Date(s) : 07/11/2023 iCal
15 h 00 min - 16 h 00 min

We say that an infinite word $u$ on a $d$ -ary alphabet has the well distributed occurrences property if, for each factor $w$ of $u$ , each positive integer $m$ , and each vector $v \in Z_{m}^{d}$ , there is an occurrence of $w$ such that the Parikh vector of the prefix of $u$ preceding such occurrence is congruent to $v$ modulo $m$ . In this talk we will discuss how aperiodic infinite words with well distributed occurrences can be used to produce aperiodic pseudorandom number generators with good statistical behavior. We study the well distributed occurrences property for certain families of infinite words including words generated by morphisms, Sturmian words and Arnoux–Rauzy words. The talk is based on new and old results..

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