代换序列研究概况

Sequences of Substitutions and Related Topics

代换序列的研究可追溯到Thue在1906年的工作,在这一工作中,他引入了一个由代换生成的序列(现称为Thue-Morse序列),研究了它的组合性质,给出了若干非重复序列的例子.大半个世纪以来,人们在各个不同的领域的研究中,从各个不同的角度一再地引入该序列并且不断地加以推广,从而引起了对一般的代换序列的研究.在六十和七十年代,这种研究主要集中在与动力系统和自动机理论的联系及其应用上.八十年代以来。

During the recent years, a great deal of progress has been made for the study of sequences of substitutions, and more and more applications and relations to other fields are discovered. This paper is devoted to a survey of this field. It contains four parts, preliminaries and the fundamental theorem (1); three typical 2-automatic sequences and their properties (2); Applications and relations to other fields (3); some generalized sequences of substitutions (4). A detailed list of references is given at the end