Frequences in self-descriptive sequences
Date(s) : 13/05/2025 iCal
11h00 - 12h00
The Oldenburger-Kolakoski sequence is the only 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 sequence admits a frequency of 1/2 for the letter « 1 ». In an attempt to tackle this problem, we consider the class of sequences which can be decomposed into a sequence of single-letters factors such that the length of the i-th factor is equal to the i-th letter of the sequence. Such a sequence is said to be self-descriptive. Denoting O = (xᵢ)_{i∈ℕ} the self-descriptive sequence and (wᵢ)_{i∈ℕ} its factors decomposition, we then define T the « directing sequence » of O such that the i-th letter of T is the one that makes up wᵢ. A natural bijection thus emerges between self-descriptive 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 analytic approach. This talk is joint work with Shigeki Akiyama, Damien Jamet and Irène Marcovici.
Emplacement
I2M Luminy - TPR2, Salle de Séminaire 304-306 (3ème étage)
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