Note on occurrences of factors in circular words

Arnoux, Pierre

doi:10.1051/ita/2016019

Arnoux, Pierre ¹

¹ Institute of mathematics, CNRS UPR 9016, Marseille, France.

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 50 (2016) no. 2, pp. 167-170.

Résumé

We give an elementary proof of a property discovered by Xavier Grandsart: let $W$ be a circular binary word; then the differences in the number of occurrences ${| W |}_{0011} - {| W |}_{1100}$ , ${| W |}_{1101} - {| W |}_{1011}$ , ${| W |}_{1010} - {| W |}_{0101}$ and ${| W |}_{0100} - {| W |}_{0010}$ are equal; this property is easily generalized using the De Bruijn graph.

Reçu le : 2016-06-12
Accepté le : 2016-09-05

MR Zbl

DOI : 10.1051/ita/2016019

Classification : 68R15
Mots-clés : Circular words, factors, De Bruijn graphs

Affiliations des auteurs :

Arnoux, Pierre ¹

¹ Institute of mathematics, CNRS UPR 9016, Marseille, France.

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     author = {Arnoux, Pierre},
     title = {Note on occurrences of factors in circular words},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {167--170},
     publisher = {EDP-Sciences},
     volume = {50},
     number = {2},
     year = {2016},
     doi = {10.1051/ita/2016019},
     mrnumber = {3580109},
     zbl = {1429.68200},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ita/2016019/}
}

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Arnoux, Pierre. Note on occurrences of factors in circular words. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 50 (2016) no. 2, pp. 167-170. doi : 10.1051/ita/2016019. http://www.numdam.org/articles/10.1051/ita/2016019/

Bibliographie
Cité par

J. Cassaigne, Private communication.

J. Cassaigne, J. Karhumäki and A. Saarela, On growth and fluctuation of $k$ -abelian complexity, Proc. of the 10th CSR. In Vol. 9139 of Lect. Notes Comput. Sci. Springer (2015) 109–122. | MR

A. Costa, Solution for the problem of the game heads or tails. Available at (2010). | arXiv

P. Deligne, letter to Xavier Grandsart.

M. Younan, Letter to Xavier Grandsart.

Cité par Sources :