Bispecial Factors in the Thue-Morse-like Sequence

Abstract

This paper investigates the structural combinatorics on words through a detailed study of the ternary Thue-Morse
like sequence, denoted by t2,3. Rooted in the framework of symbolic dynamics and automatic sequences, our objective
is to characterize its global and local properties. First, we establish essential combinatorial features of t2,3, focusing on its special factors and recurrent patterns. Second, we provide a complete classification of its bispecial factors, determining their types, lengths, and exact evolution. Finally,these structural insights allow us to explicitly characterize the tri-extendable factors of the sequence. These results of fer deep insights into the language geometry of non-binary morphic sequences.