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.
Mots-clés : permutation, infinite permutation, ordering, infinite word, automatic word, automatic permutation, Thue-Morse word, Thue-Morse permutation
@article{ITA_2012__46_1_77_0,
author = {Frid, Anna and Zamboni, Luca},
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://archive.numdam.org/articles/10.1051/ita/2011129/}
}
TY - JOUR AU - Frid, Anna AU - Zamboni, Luca TI - On automatic infinite permutations JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2012 SP - 77 EP - 85 VL - 46 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita/2011129/ DO - 10.1051/ita/2011129 LA - en ID - ITA_2012__46_1_77_0 ER -
%0 Journal Article %A Frid, Anna %A Zamboni, Luca %T On automatic infinite permutations %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2012 %P 77-85 %V 46 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita/2011129/ %R 10.1051/ita/2011129 %G en %F ITA_2012__46_1_77_0
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. http://archive.numdam.org/articles/10.1051/ita/2011129/
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