Geodesic
Full and Uniform Sequences
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical logic and algebra, Tome 242 (2003), pp. 141-146 
A. Carpi; A. de Luca. Full and Uniform Sequences. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical logic and algebra, Tome 242 (2003), pp. 141-146. http://geodesic.mathdoc.fr/item/TM_2003_242_a11/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The point of view that we follow in this paper is to get information on the structure of a word $w$ by considering some suitable conditions on the number of occurrences in $w$ of any other word $u$. In this framework, two notions are very natural and of great interest, the fullness and the uniformity of a word. We study some properties of these notions.

[1] Carpi A., de Luca A., “Words and special factors”, Theor. Comput. Sci., 259 (2001), 145–182 | DOI | MR | Zbl

[2] Carpi A., de Luca A., “Uniform words”, Adv. Appl. Math. (to appear)

[3] de Bruijn N. G., “A combinatorial problem”, Proc. Ned. Akad. Wet., 49 (1946), 758–764 | MR

[4] Fredricksen H., “A survey of full length nonlinear shift register cycle algorithms”, SIAM Rev., 24 (1982), 195–221 | DOI | MR | Zbl

[5] Lothaire M., Combinatorics on words, 2nd ed., Cambridge Math. Library, Cambridge Univ. Press, Cambridge, 1997 | MR | Zbl

[6] Marshall A. W., Olkin I., Inequalities: Theory of majorization and its applications, Acad. Press, New York, 1979 | MR