Let be an integer. In terms of combinatorics on words we describe all irrational numbers with the property that the fractional parts , , all belong to a semi-open or an open interval of length . The length of such an interval cannot be smaller, that is, for irrational ξ, the fractional parts , , cannot all belong to an interval of length smaller than .
Soit un entier. Au moyen de résultats de la combinatoire des mots, nous caractérisons l'ensemble des nombres réels tels que les parties fractionnaires , , appartiennent toutes à un intervalle semi-ouvert ou ouvert de longueur . La longueur d'un tel intervalle ne peut pas être plus petite, c'est-à-dire, quel que soit le nombre irrationnel ξ, aucun intervalle de longueur strictement inférieure à ne contient toutes les parties fractionnaires , .
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@article{CRMATH_2005__341_2_69_0, author = {Bugeaud, Yann and Dubickas, Art\={u}ras}, title = {Fractional parts of powers and {Sturmian} words}, journal = {Comptes Rendus. Math\'ematique}, pages = {69--74}, publisher = {Elsevier}, volume = {341}, number = {2}, year = {2005}, doi = {10.1016/j.crma.2005.06.007}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2005.06.007/} }
TY - JOUR AU - Bugeaud, Yann AU - Dubickas, Artūras TI - Fractional parts of powers and Sturmian words JO - Comptes Rendus. Mathématique PY - 2005 SP - 69 EP - 74 VL - 341 IS - 2 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2005.06.007/ DO - 10.1016/j.crma.2005.06.007 LA - en ID - CRMATH_2005__341_2_69_0 ER -
%0 Journal Article %A Bugeaud, Yann %A Dubickas, Artūras %T Fractional parts of powers and Sturmian words %J Comptes Rendus. Mathématique %D 2005 %P 69-74 %V 341 %N 2 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2005.06.007/ %R 10.1016/j.crma.2005.06.007 %G en %F CRMATH_2005__341_2_69_0
Bugeaud, Yann; Dubickas, Artūras. Fractional parts of powers and Sturmian words. Comptes Rendus. Mathématique, Volume 341 (2005) no. 2, pp. 69-74. doi : 10.1016/j.crma.2005.06.007. http://archive.numdam.org/articles/10.1016/j.crma.2005.06.007/
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Cited by Sources:
⁎ The research of the first named author was supported by the Austrian Science Foundation FWF, grant M822-N12. The research of the second named author was partially supported by the Lithuanian State Science and Studies Foundation.