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UID:7964@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20151124T110000
DTEND;TZID=Europe/Paris:20151124T120000
DTSTAMP:20241120T205616Z
URL:https://www.i2m.univ-amu.fr/evenements/multiple-tilings-associated-to-
 the-symmetric-b-expansions/
SUMMARY:Tomáš Hejda (CTU in Prague): Multiple tilings associated to the s
 ymmetric β-expansions
DESCRIPTION:Tomáš Hejda: It is a well-known fact that when β is a d-Bona
 cci number\, the Rauzy fractals arising from the greedy (Rényi) β-transf
 ormation tile the contracting hyperplane. Recently\, it was shown that all
  Pisot units satisfy this (the so-called Pisot conjecture for β-numeratio
 n\; proved by M. Barge). However\, the Rauzy fractals arising from the sym
 metric Tribonacci transformation form a double tiling\, i.e.\, almost ever
 y point of the hyperplane lies in exactly 2 tiles. This means that the Pis
 ot conjecture for beta-numeration is not true for symmetric transformation
 s.\nWe show that for the d-Bonacci numbers\, the degree of the multiple ti
 ling (MT) is d-1. We can also determine which tiles form each layer of the
  multiple tiling. This relates to toral automorphisms\; in the case when t
 he MT is a tiling\, the natural extension of the transformation is a toral
  automorphism.\nFor general Pisot unit bases 1&lt\;β&lt\;2\, we show show
  how to compute the degree of the MT from the degree of the MT of a differ
 ent transformation. We also show a necessary condition for the MT to be a 
 tiling.\nhttps://link.springer.com/content/pdf/10.1007/s00605-018-1219-2.p
 df\n\n&nbsp\;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Tomas_Hejda.jpg
CATEGORIES:Séminaire,Ernest
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DTSTART:20151025T020000
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