Journée-séminaire de combinatoire

(équipe CALIN du LIPN, université Paris-Nord, Villetaneuse)

Le 17 janvier 2023 à 14h00 en B107 & visioconférence, Wolfgang Steiner nous parlera de : Shift spaces defined by lexicographic inequalities and unique double base expansions

Résumé : Beta-expansions are generalisations of the usual decimal or binary expansions to real bases. Instead of taking powers of a single base, we use powers of two bases where the exponents depend on the choice of the (binary) digit sequence. We study the question when such expansions are unique and give a characterisation of the pairs of bases that admit non-trivial unique expansions or even uncountably many unique expansions. This is directly related to the question when a binary shift defined by two lexicographic inequalities is non-trivial or uncountable, and the characterisation is in terms of S-adic words, where S consists of the Sturmian substitutions and the Thue-Morse substitution. This is joint work with Vilmos Komornik and Yuru Zou.

 [Slides.pdf] [arXiv] [vidéo]

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