A characterization of the squares in a Fibonacci string
TLDR
This paper provides a characterization of all the squares in F, hence in every prefix Fn; this characterization naturally gives rise to a algorithm which specifiesall the squares of Fn in an appropriate encoding.About:
This article is published in Theoretical Computer Science.The article was published on 1997-02-10 and is currently open access. It has received 88 citations till now. The article focuses on the topics: Fibonacci number & String (computer science).read more
Citations
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Proceedings ArticleDOI
Finding maximal repetitions in a word in linear time
Roman Kolpakov,Gregory Kucherov +1 more
TL;DR: This work proves a combinatorial result asserting that the sum of exponents of all maximal repetitions of a word of length n is bounded by a linear function in n, which implies that there is only a linear number of maximal repetition in a word.
Book ChapterDOI
On Maximal Repetitions in Words
Roman Kolpakov,Gregory Kucherov +1 more
TL;DR: It is proved that the maximal number of maximal repetitions in general words (on arbitrary alphabet) of length n is linearly-bounded in n, and some applications and consequences are mentioned.
Journal ArticleDOI
Simple and flexible detection of contiguous repeats using a suffix tree
Jens Stoye,Dan Gusfield +1 more
TL;DR: This paper first gives a simple time- and space- optimal algorithm to find all tandem repeats, and then modify it to become a time-and-space-optimal algorithm for finding only the primitive tandem repeats.
Journal Article
The number of runs in a string : Improved analysis of the linear upper bound
TL;DR: In this article, the authors proposed a new approach to the analysis of runs based on the properties of subperiods: the periods of periodic parts of the runs of a string.
Journal ArticleDOI
Maximal repetitions in strings
Maxime Crochemore,Lucian Ilie +1 more
TL;DR: Improve dramatically the previous results by proving that c=<1.6 and showing how it could be improved by computer verification down to 1.18 or less and for the stronger result concerning the linearity of the sum of exponents, the first explicit bound is given.
References
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Book
The Art of Computer Programming
TL;DR: The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid.
Journal ArticleDOI
Identification of common molecular subsequences.
TL;DR: This letter extends the heuristic homology algorithm of Needleman & Wunsch (1970) to find a pair of segments, one from each of two long sequences, such that there is no other Pair of segments with greater similarity (homology).
Journal ArticleDOI
Fast Pattern Matching in Strings
TL;DR: An algorithm is presented which finds all occurrences of one given string within another, in running time proportional to the sum of the lengths of the strings, showing that the set of concatenations of even palindromes, i.e., the language $\{\alpha \alpha ^R\}^*$, can be recognized in linear time.
Book
Handbook of theoretical computer science
TL;DR: The Handbook of Theoretical Computer Science provides professionals and students with a comprehensive overview of the main results and developments in this rapidly evolving field.
Book
History of the Theory of Numbers
Abstract: THE third and concluding volume of Prof. Dickson's great work deals first with the arithmetical. theory of binary quadratic forms. A long chapter on the class-number is contributed by Mr. G. H. Cresse. Next comes an account of existing knowledge on quadratic forms in three or more variables, followed by chapters on cubic forms, Hermitian and bilinear forms, and modular invariants and covariants.History of the Theory of Numbers.Prof. Leonard Eugene Dickson. Vol. 3: Quadratic and Higher Forms. With a Chapter on the Class Number by G. H. Cresse. (Publication No. 256.) Pp. v + 313. (Washington: Carnegie Institution, 1923.) 3.25 dollars.