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.

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 :
Accepté le :
DOI : 10.1051/ita/2016019
Classification : 68R15
Mots clés : Circular words, factors, De Bruijn graphs
Arnoux, Pierre 1

1 Institute of mathematics, CNRS UPR 9016, Marseille, France.
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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://archive.numdam.org/articles/10.1051/ita/2016019/

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.

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