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SUMMARY:Émilie Charlier (Université de Liège)
DTSTART:20220524T123000Z
DTEND:20220524T133000Z
DTSTAMP:20260423T052928Z
UID:OWNS/86
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/86/">Sp
 ectrum\, algebraicity and normalization in alternate bases</a>\nby Émilie
  Charlier (Université de Liège) as part of One World Numeration seminar\
 n\n\nAbstract\nThe first aim of this work is to give information about the
  algebraic properties of alternate bases determining sofic systems. We exh
 ibit two conditions: one necessary and one sufficient. Comparing the setti
 ng of alternate bases to that of one real base\, these conditions exhibit 
 a new phenomenon: the bases should be expressible as rational functions of
  their product. The second aim is to provide an analogue of Frougny's resu
 lt concerning normalization of real bases representations. Under some suit
 able condition (i.e.\, our previous sufficient condition for being a sofic
  system)\, we prove that the normalization function is computable by a fin
 ite Büchi automaton\, and furthermore\, we effectively construct such an 
 automaton. An important tool in our study is the spectrum of numeration sy
 stems associated with alternate bases. For our purposes\, we use a general
 ized concept of spectrum associated with a complex base and complex digits
 \, and we study its topological properties. \n\nThis is joint work with C
 élia Cisternino\, Zuzana Masáková and Edita Pelantová.\n
LOCATION:https://researchseminars.org/talk/OWNS/86/
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