A counterexample to a question of Hof, Knill and Simon
S\'ebastien Labb\'e
TL;DR
This paper provides a counterexample to a question about the properties of purely morphic sequences with infinitely many palindromes, extending previous binary alphabet results to ternary alphabets.
Contribution
It presents the first known counterexample on the ternary alphabet, answering a question posed by Hof, Knill, and Simon in 1995.
Findings
Counterexample exists on the ternary alphabet
Extends previous binary alphabet results
Answers a long-standing open question
Abstract
In this article, we give a negative answer to a question of Hof, Knill and Simon (1995) concerning purely morphic sequences obtained from primitive morphism containing an infinite number of palindromes. Proven for the binary alphabet by B. Tan in 2007, we show the existence of a counterexample on the ternary alphabet.
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