کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6872624 | 684166 | 2012 | 12 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Sturmian graphs and integer representations over numeration systems
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موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
In this paper we consider a numeration system, originally due to Ostrowski, based on the continued fraction expansion of a real number α. We prove that this system has deep connections with the Sturmian graph associated with α. We provide several properties of the representations of the natural integers in this system. In particular, we prove that the set of lazy representations of the natural integers in this numeration system is regular if and only if the continued fraction expansion of α is eventually periodic. The main result of the paper is that for any number i the unique path weighted i in the Sturmian graph associated with α represents the lazy representation of i in the Ostrowski numeration system associated with α.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Applied Mathematics - Volume 160, Issues 4â5, March 2012, Pages 536-547
Journal: Discrete Applied Mathematics - Volume 160, Issues 4â5, March 2012, Pages 536-547
نویسندگان
C. Epifanio, C. Frougny, A. Gabriele, F. Mignosi, J. Shallit,