We study infinite binary words that contain few distinct palindromes. In particular, we classify such words according to their critical exponents. This extends results by Fici and Zamboni [TCS 2013]. Interestingly, the words with 18 and 20 palindromes happen to be morphic images of the fixed point of the morphism 0↦01, 1↦21, 2↦0.
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Dvořáková et al. (2024) studied this question.
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