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UID:8610@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20250513T110000
DTEND;TZID=Europe/Paris:20250513T120000
DTSTAMP:20250508T093722Z
URL:https://www.i2m.univ-amu.fr/evenements/tran-cong/
SUMMARY:Mai-Linh Tran-Cong (...): Frequences in self-descriptive sequences
DESCRIPTION:Mai-Linh Tran-Cong: The Oldenburger-Kolakoski sequence is the o
 nly infinite sequence over the alphabet {1\,2} starting with a « 1 » and
  equal to its own derivative. M.S. Keane conjectured in 1991 that this seq
 uence admits a frequency of 1/2 for the letter «1».\nIn an attempt to ta
 ckle this problem\, we consider the class of sequences which can be decomp
 osed into a sequence of single-letter factors such that the length of the 
 iᵗʰ factor is equal to the iᵗʰ letter of the sequence. Such a sequen
 ce is said to be self-descriptive.\nDenoting O≔(xᵢ)_{i∈ℕ} the self
 -descriptive sequence and (wᵢ)_{i∈ℕ} its factor decomposition\, we t
 hen define the «directing sequence» T of O\, whose iᵗʰ letter is the 
 one that makes up wᵢ. A natural bijection thus emerges between self-desc
 riptive sequences and their directing sequences. Using this bijection\, we
  are able to compute frequences in some self-descriptive sequences through
  both a probabilistic (Boisson\, Jamet\, Marcovici — 2024) and an analyt
 ic approach.\nThis talk is joint work with Shigeki Akiyama\, Damien Jamet 
 and Irène Marcovici.
CATEGORIES:Séminaire,Ernest
LOCATION:I2M Luminy - TPR2\, Salle de Séminaire 304-306 (3ème étage)\, 1
 63 Avenue de Luminy\, Marseille\, 13009\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=163 Avenue de Luminy\, Mars
 eille\, 13009\, France;X-APPLE-RADIUS=100;X-TITLE=I2M Luminy - TPR2\, Sall
 e de Séminaire 304-306 (3ème étage):geo:0,0
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