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SUMMARY:Complexités des mots de billard hypercubique
DTSTART;VALUE=DATE-TIME:20221115T094500Z
DTEND;VALUE=DATE-TIME:20221115T104500Z
DTSTAMP;VALUE=DATE-TIME:20230206T161600Z
UID:indico-event-8822@indico.math.cnrs.fr
DESCRIPTION:Speakers: Mélodie Andrieu\n\nSturmian words (1940) form a cla
ss of infinite words over the binary alphabet which sheds light on the rem
arkable interactions between combinatorics\, dynamical systems and number
theory. These interactions are reflected in the various ways to define the
m. For instance\, Sturmian words are equivalently - words with factor
ial complexity n + 1\, i.e.\, admitting exactly n + 1 factors of length n
for all n (a factor of w of length n is a subword of w written with n cons
ecutive letters)\; - binary aperiodic words with imbalance equal to 1
: all factors of a given length contain\, up to a difference of one\, the
same numbers of 1s (and thus as well\, the same numbers of 2s)\; - th
e symbolic trajectories of a ball in a square billiard\, launched with a m
omentum with rationally independent entries.They give birth to several gen
eralizations on the d−letter alphabet for d ≥ 3\, depending on the con
sidered definition (e.g. : Arnoux-Rauzy or episturmian words\, words assoc
iated with other d−dimensional continued fraction algorithms\, polygonal
or cubic billiard words\, etc.) A large program\, initiated by Rauzy in t
he 80s\, is to determine which properties are still equivalent in higher d
imension\, and which are not.In this talk\, I will focus on two combinator
ial quantities\, the factorial and abelian complexities\, for words genera
ted by a billiard in a cube of dimension d.\n\nhttps://indico.math.cnrs.fr
/event/8822/
LOCATION:ICJ\, Bât. Braconnier
URL:https://indico.math.cnrs.fr/event/8822/
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