Repetitions in infinite palindrome-rich words
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 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.
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