A palindromization map for the free group |
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Authors: | Christian Kassel Christophe Reutenauer |
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Affiliation: | 1. Université de Strasbourg, Institut de Recherche Mathématique Avancée, CNRS - Université Louis Pasteur, 7 rue René Descartes, 67084 Strasbourg, France;2. Mathématiques, Université du Québec à Montréal, Montréal, CP 8888, succ. Centre Ville, Canada H3C 3P8 |
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Abstract: | We define a self-map Pal:F2→F2 of the free group on two generators a,b, using automorphisms of F2 that form a group isomorphic to the braid group B3. The map Pal restricts to de Luca’s right iterated palindromic closure on the submonoid generated by a,b. We show that Pal is continuous for the profinite topology on F2; it is the unique continuous extension of de Luca’s right iterated palindromic closure to F2. The values of Pal are palindromes and coincide with the elements g∈F2 such that abg and bag are conjugate. |
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Keywords: | Word Palindrome Free group Automorphism Braid group Profinite topology |
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