论文信息 - Minimal Duval Extensions

Minimal Duval Extensions

A word v=wu is a (nontrivial) Duval extension of the unbordered word w, if (u is not a prefix of v and) w is an unbordered factor of v of maximum length. After a short survey of the research topic related to Duval extensions, we show that, if wu is a minimal Duval extension, then u is a factor of w. We also show that finite, unbordered factors of Sturmian words are Lyndon words.

Tero Harju | Dirk Nowotka

[1] G. A. Hedlund,et al. Symbolic Dynamics II. Sturmian Trajectories , 1940 .

[2] M. Lothaire,et al. Algebraic Combinatorics on Words: Index of Notation , 2002 .

[3] Maurice Pouzet,et al. Une caracterisation des mots periodiques , 1979, Discret. Math..

[4] Jean-Pierre Duval,et al. Relationship between the period of a finite word and the length of its unbordered segments , 1982, Discret. Math..

[5] M. Lothaire. Algebraic Combinatorics on Words , 2002 .

[6] R. Baer,et al. The Significance of the System of Subgroups for the Structure of the Group , 1939 .

[7] Filippo Mignosi,et al. A Note on a Conjecture of Duval and Sturmian Words , 2002, RAIRO Theor. Informatics Appl..

[8] Aldo de Luca,et al. Sturmian Words, Lyndon Words and Trees , 1997, Theor. Comput. Sci..

[9] Jean-Pierre Borel,et al. Quelques mots sur la droite projective réelle , 1993 .

[10] Andrzej Ehrenfeucht,et al. Periodicity and unbordered segments of words , 1979, Discret. Math..

[11] Guy Melançon. Lyndon Words and Singular Factors of Sturmian Words , 1999, Theor. Comput. Sci..

[12] R. Lyndon. On Burnside’s problem , 1954 .