Order type of shifts of morphic words

Abstract: The shifts of an infinite word $W=a_0a_1\cdots$ are the words $W_i=a_ia_{i+1}\cdots$. As a measure of the complexity of a word $W$, we consider the order-type of the set of shifts, ordered lexicographically. We will look at the order-type of shifts of morphic words over a finite alphabet that are not ultimately periodic. As a concrete example, we give the explicit ordering among shifts of the Thue-Morse word. The order type of shifts of the Fibonacci word will be discussed. We then give special consideration to uniform morphisms on 3 letters.

number theory

Audience: researchers in the discipline

Combinatorial and additive number theory (CANT 2022)