Geodesic
On automatic infinite permutations
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 1, pp. 77-85

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An infinite permutation α is a linear ordering of N. We study properties of infinite permutations analogous to those of infinite words, and show some resemblances and some differences between permutations and words. In this paper, we try to extend to permutations the notion of automaticity. As we shall show, the standard definitions which are equivalent in the case of words are not equivalent in the context of permutations. We investigate the relationships between these definitions and prove that they constitute a chain of inclusions. We also construct and study an automaton generating the Thue-Morse permutation.

DOI : 10.1051/ita/2011129
Classification : 05A05, 68R15
Keywords: permutation, infinite permutation, ordering, infinite word, automatic word, automatic permutation, Thue-Morse word, Thue-Morse permutation 
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     title = {On automatic infinite permutations},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {77--85},
     publisher = {EDP-Sciences},
     volume = {46},
     number = {1},
     year = {2012},
     doi = {10.1051/ita/2011129},
     mrnumber = {2904962},
     zbl = {1247.05007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ita/2011129/}
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Frid, Anna; Zamboni, Luca. On automatic infinite permutations. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 1, pp. 77-85. doi: 10.1051/ita/2011129

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