کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4654665 1632831 2008 19 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On an involution of Christoffel words and Sturmian morphisms
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
On an involution of Christoffel words and Sturmian morphisms
چکیده انگلیسی

There is a natural involution on Christoffel words, originally studied by the second author in [A. de Luca, Combinatorics of standard Sturmian words, Lecture Notes in Computer Science 1261 (1997) 249–267]. We show that it has several equivalent definitions: one of them uses the slope of the word, and changes the numerator and the denominator respectively in their inverses modulo the length; another one uses the cyclic graph allowing the construction of the word, by interpreting it in two ways (one as a permutation and its ascents and descents, coded by the two letters of the word, the other in the setting of the Fine and Wilf periodicity theorem); a third one uses central words and generation through iterated palindromic closure, by reversing the directive word. We show further that this involution extends to Sturmian morphisms, in the sense that it preserves conjugacy classes of these morphisms, which are in bijection with Christoffel words. The involution on morphisms is the restriction of some conjugation of the automorphisms of the free group. Finally, we show that, through the geometrical interpretation of substitutions of Arnoux and Ito, our involution is the same thing as duality of endomorphisms (modulo some conjugation).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: European Journal of Combinatorics - Volume 29, Issue 2, February 2008, Pages 535–553
نویسندگان
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