On the Zero Defect Conjecture |
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| Institution: | 1. Université de Liège, Bât. B37 Institut de Mathématiques, Grande Traverse 12, 4000 Liège, Belgium;2. Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Czech Republic;3. Faculty of Information Technology, Czech Technical University in Prague, Czech Republic |
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| Abstract: | Brlek et al., conjectured in 2008 that any fixed point of a primitive morphism with finite palindromic defect is either periodic or its palindromic defect is zero. Bucci and Vaslet disproved this conjecture in 2012 by a counterexample over ternary alphabet. We prove that the conjecture is valid on binary alphabet. We also describe a class of morphisms over multiliteral alphabet for which the conjecture still holds. The proof is based on properties of extension graphs. |
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