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SUMMARY:Wolfgang Steiner (CNRS\, Université de Paris)
DTSTART:20220215T133000Z
DTEND:20220215T143000Z
DTSTAMP:20260423T021216Z
UID:OWNS/77
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/77/">Un
 ique double base expansions</a>\nby Wolfgang Steiner (CNRS\, Université d
 e Paris) as part of One World Numeration seminar\n\n\nAbstract\nFor pairs 
 of real bases $\\beta_0\, \\beta_1 > 1$\, we study expansions of the form\
 n$\\sum_{k=1}^\\infty i_k / (\\beta_{i_1} \\beta_{i_2} \\cdots \\beta_{i_k
 })$\nwith digits $i_k \\in \\{0\,1\\}$.\nWe characterise the pairs admitti
 ng non-trivial unique expansions as well as those admitting uncountably ma
 ny unique expansions\, extending recent results of Neunhäuserer (2021) an
 d Zou\, Komornik and Lu (2021).\nSimilarly to the study of unique $\\beta$
 -expansions with three digits by the speaker (2020)\, this boils down to d
 etermining the cardinality of binary shifts defined by lexicographic inequ
 alities.\nLabarca and Moreira (2006) characterised when such a shift is em
 pty\, at most countable or uncountable\, depending on the position of the 
 lower and upper bounds with respect to Thue-Morse-Sturmian words. \n\nThis
  is joint work with Vilmos Komornik and Yuru Zou.\n
LOCATION:https://researchseminars.org/talk/OWNS/77/
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