On Families of Limit S-adic Words (Invited Talk)

摘要

Given a set S of morphisms, an infinite word is limit S-adic if it can be recursively desubstituted using morphisms in 5. Substitutive-adicity arises naturally in various studies especially in studies on infinite words with factor complexity bounded by an affine function. In the literature, when a family F of infinite words defined by a combinatorial property P appears to be 5-adic for some set S of morphisms, it is very rare that the whole set of limit 5-adic words coincides with F. The aim of the talk is to survey such situations in which necessarily morphisms of S preserve the property P of infinite words.