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UID:5900@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20221028T110000
DTEND;TZID=Europe/Paris:20221028T120000
DTSTAMP:20241120T200651Z
URL:https://www.i2m.univ-amu.fr/evenements/complexities-of-hypercubic-bill
 iard-words-answering-a-question-of-rauzy/
SUMMARY:Mélodie Andrieu  (Université Bar-Ilan\, Israel): Complexities of 
 hypercubic billiard words (answering a question of Rauzy)
DESCRIPTION:Mélodie Andrieu : Sturmian words (1940) form a class of infini
 te words over the binary alphabet which sheds light on the remarkable inte
 ractions between combinatorics\, dynamical systems and number theory. Thes
 e interactions are reflected in the various ways to define them. For insta
 nce\, Sturmian words are equivalently\n- words with factorial complexity n
  + 1\, i.e.\, admitting exactly n + 1 factors of length n for all n (a fac
 tor of w of length n is a subword of w written with n consecutive letters)
 \;\n- binary aperiodic words with imbalance equal to 1: all factors of a g
 iven length contain\, up to a difference of one\, the same numbers of 1s (
 and thus as well\, the same numbers of 2s)\;\n- the symbolic trajectories 
 of a ball in a square billiard\, launched with a momentum with rationally 
 independent entries.\n\nThey give birth to several generalizations on the 
 d−letter alphabet for d ≥ 3\, depending on the considered definition (
 e.g. : Arnoux-Rauzy or episturmian words\, words associated with other d
 −dimensional continued fraction algorithms\, polygonal or cubic billiard
  words\, etc.) A large program\, initiated by Rauzy in the 80s\, is to det
 ermine which properties are still equivalent in higher dimension\, and whi
 ch are not.\n\nIn this talk\, I will focus on two combinatorial quantities
 \, the factorial and abelian complexities\, for words generated by a billi
 ard in a cube of dimension d.\n\n[Based on a joint work with Léo Vivion.]
 \n\n&nbsp\;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 022/10/Melodie_Andrieu.png
CATEGORIES:Séminaire,Rauzy
LOCATION:Saint-Charles - FRUMAM  (2ème étage)\, 3 Place Victor Hugo\, Mar
 seille\, 13003\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=3 Place Victor Hugo\, Marse
 ille\, 13003\, France;X-APPLE-RADIUS=100;X-TITLE=Saint-Charles - FRUMAM  (
 2ème étage):geo:0,0
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