Instituto de Matemática e Estatística | IME-USP
Evento
- Título:
- Seminário de Sistemas Dinâmicos: Extracting subsequences from the Thue-Morse Sequence
- Quando:
- 08.05.2012 14.00 h
- Onde:
- Auditório Antonio Gilioli, bloco A - Cidade Universitária - São Paulo
- Categoria:
- MAP - Seminarios
Descrição
Prof. Dr. CHRISTIAN MAUDUIT (IMPA – RJ)
Abstract
“Let T = t_0 t_1 ... t_n ... \in \{0,1\}^\N be the Thue Morse sequence (i.e. the infinite word T obtained as the limit in \{0,1\}^\N of the sequence of finite words (T_k)_{k \in \N} defined by the recursion T_0 = 0 , T'_0 = 1 and T_{k+1} = T_k T'_k , T'_{k+1} = T'_k T_k for any non negative integer k). Our talk concerns the study of statistical properties of the subsequences (T_{u_k})_{k \in \N}, where u = (u_k)_{k \in \N} is a given increasing sequence of integers. This problem can easily be translated in the study of the representation of elements of the sequence u with an even (or odd) sum of digits in base 2. We will focus on recent results and open problems concerning the case where u is the sequence of prime numbers or the sequence of square numbers "