Repetitions in Infinite Palindrome-Rich Words
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Abstract
Rich words are those 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 consider 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 \(\varSigma _2=\{0,1\}\) with a small critical exponent of \(2+\sqrt{2}/2\). This represents the first progress on an open problem of Vesti from 2017.
Keywords
Critical exponent Repetitions Rich words PalindromeNotes
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