# On automatic infinite permutations∗

RAIRO - Theoretical Informatics and Applications (2012)

- Volume: 46, Issue: 1, page 77-85
- ISSN: 0988-3754

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topFrid, Anna, and Zamboni, Luca. "On automatic infinite permutations∗." RAIRO - Theoretical Informatics and Applications 46.1 (2012): 77-85. <http://eudml.org/doc/277836>.

@article{Frid2012,

abstract = {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.},

author = {Frid, Anna, Zamboni, Luca},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Permutation; infinite permutation; ordering; infinite word; automatic word; automatic permutation; Thue-Morse word; Thue-Morse permutation; permutation},

language = {eng},

month = {3},

number = {1},

pages = {77-85},

publisher = {EDP Sciences},

title = {On automatic infinite permutations∗},

url = {http://eudml.org/doc/277836},

volume = {46},

year = {2012},

}

TY - JOUR

AU - Frid, Anna

AU - Zamboni, Luca

TI - On automatic infinite permutations∗

JO - RAIRO - Theoretical Informatics and Applications

DA - 2012/3//

PB - EDP Sciences

VL - 46

IS - 1

SP - 77

EP - 85

AB - 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.

LA - eng

KW - Permutation; infinite permutation; ordering; infinite word; automatic word; automatic permutation; Thue-Morse word; Thue-Morse permutation; permutation

UR - http://eudml.org/doc/277836

ER -

## References

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- M. Makarov, On an infinite permutation similar to the Thue-Morse word. Discrete Math.309 (2009) 6641–6643.
- M. Makarov, On the permutations generated by Sturmian words. Sib. Math. J.50 (2009) 674–680.
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- S. Widmer, Permutation complexity of the Thue-Morse word. Adv. Appl. Math.47 (2011) 309–329.

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