Repetitions in infinite palindrome-rich words

Aseem Raj Baranwal; Jeffrey Shallit

doi:10.1007/978-3-030-28796-2_7

paper

Repetitions in infinite palindrome-rich words

arXiv:1904.10028 · doi:10.1007/978-3-030-28796-2_7

Abstract

Rich words are characterized by containing the maximum possible number of distinct palindromes. Several characteristic properties of rich words have been studied; yet the analysis of repetitions in rich words still involves some interesting open problems. We address lower bounds on the repetition threshold of infinite rich words over 2 and 3-letter alphabets, and construct a candidate infinite rich word over the alphabet $Σ_{2} = {0, 1}$ with a small critical exponent of $2 + 2 /2$ . This represents the first progress on an open problem of Vesti from 2017.

12 pages