Periods and Binary Words
نویسندگان
چکیده
We give an elementary short proof for a well-known theorem of Guibas and Odlyzko stating that the sets of periods of words are independent of the alphabet size. As a consequence of our constructing proof, we give a linear time algorithm which, given a word, computes a binary one with the same periods. We give also a very short proof for the famous Fine and Wilf's periodicity lemma.
منابع مشابه
A particle swarm optimization method for periodic vehicle routing problem with pickup and delivery in transportation
In this article, multiple-product PVRP with pickup and delivery that is used widely in goods distribution or other service companies, especially by railways, was introduced. A mathematical formulation was provided for this problem. Each product had a set of vehicles which could carry the product and pickup and delivery could simultaneously occur. To solve the problem, two meta-heuristic methods...
متن کاملTHE 2-ADIC, BINARY AND DECIMAL PERIODS OF 1/3k APPROACH FULL COMPLEXITY FOR INCREASING k
An infinite word x over an alphabet with b letters has full complexity if for each m ∈ N all the bm words of length m are factors of x. We prove that the periods of ±1/3k in the 2-adic expansion approach full complexity for increasing k: For any m ∈ N, the periods for k > "(m + 1)ln(2)/ln(3)# have complexity 2m. Amazingly, these 2m words occur in the period almost the same number of times. On t...
متن کاملCorrelations of Partial Words
Partial words are strings over a finite alphabet that may contain a number of “do not know” symbols. In this paper, we introduce the notions of binary and ternary correlations, which are binary and ternary vectors indicating the periods and weak periods of partial words. Extending a result of Guibas and Odlyzko, we characterize precisely which of these vectors represent the (weak) period sets o...
متن کاملCorrelations of Partial Words ? ( Extended
Partial words are strings over a finite alphabet that may contain a number of “do not know” symbols. In this paper, we introduce the notions of binary and ternary correlations, which are binary and ternary vectors indicating the periods and weak periods of partial words. Extending a result of Guibas and Odlyzko, we characterize precisely which of these vectors represent the (weak) period sets o...
متن کاملSturmian words and the Stern sequence
Central, standard, and Christoffel words are three strongly interrelated classes of binary finite words which represent a finite counterpart of characteristic Sturmian words. A natural arithmetization of the theory is obtained by representing central and Christoffel words by irreducible fractions labeling respectively two binary trees, the Raney (or Calkin-Wilf) tree and the Stern-Brocot tree. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 89 شماره
صفحات -
تاریخ انتشار 2000