Rapport de Recherche Litp /
Litp research reports
9 pages - Mars/March 1995 - Document en anglais.
PostScript : Ko /Kb
Titre / Title: a DIVISION PROPERTY OF THE FIBONACCi WORD
Abstract : The Fibonacci word e is the limit sequence of the infinite sequence (en)n>0 of finite words inductively defined as: e0 = b, e1 = a, en+1 = enen-1, n > 0.
We prove that e admits the factorization
e = ê3ê5.....ê2n+1.....,
where (^) denotes the reversal operation. This factorization is minimal in the following sense. Any non trivial permutation of a finite number of the above factors will produce an infinite word which is greater than e in the lexicographic order. An extension of this result to the case of standard Sturmian words is also given.
Publications internes Litp 1995 / Litp research reports 1995