1,721,005 research outputs found
Properties of a class of Toeplitz words
Full text linkWe study the properties of the uncountable set of Stewart words. These are Toeplitz words specified by infinite sequences of Toeplitz patterns of the form αβγ, where α,β,γ is any permutation of the symbols 0,1,?. We determine the critical exponent of the Stewart words, prove that they avoid the pattern xxyyxx, find all factors that are palindromes, and determine their subword complexity. An interesting aspect of our work is that we use automata-theoretic methods and a decision procedure for automata to carry out the proofs
Sturmian graphs and integer representations over numeration systems
No full textIn this paper we consider a numeration system, originally due to Ostrowski, based on the continued fraction expansion of a real number alpha. We prove that this system has deep connections with the Sturmian graph associated with alpha. 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 alpha 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 alpha represents the lazy representation of i in the Ostrowski numeration system associated with alpha
On Sturmian Graphs
No full textIn this paper we define Sturrman graphs and we prove that all of them have a certain "counting" property. We show deep connections between this counting property and two conjectures, by Moser and by Zaremba, on the continued fraction expansion of real numbers. These graphs turn out to be the underlying graphs of compact directed acyclic word graphs of central Sturtnian words. In order to prove this result, we give a characterization of the maximal repeats of central Sturmian words. We show also that, in analogy with the case of Sturmian words, these graphs converge to infinite ones
Sturmian Graphs and a conjecture of Moser
No full textIn this paper we define Sturmian graphs and we prove that all of them have a "counting" property. We show deep connections between this counting property and two conjectures, by Moser and by Zaremba, on the continued fraction expansion of real numbers. These graphs turn out to be the underlying graphs of CDAWGs of central Sturmian words. We show also that, analogously to the case of Sturmian words, these graphs converge to infinite ones
Sturmian graphs and integer representations over numeration systems
No full textAbstractIn 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
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Abelian-square-rich words
No full textAn abelian square is the concatenation of two words that are anagrams of one another. A word of length n can contain at most Θ(n2) distinct factors, and there exist words of length n containing Θ(n2) distinct abelian-square factors, that is, distinct factors that are abelian squares. This motivates us to study infinite words such that the number of distinct abelian-square factors of length n grows quadratically with n. More precisely, we say that an infinite word w is abelian-square-rich if, for every n, every factor of w of length n contains, on average, a number of distinct abelian-square factors that is quadratic in n; and uniformly abelian-square-rich if every factor of w contains a number of distinct abelian-square factors that is proportional to the square of its length. Of course, if a word is uniformly abelian-square-rich, then it is abelian-square-rich, but we show that the converse is not true in general. We prove that the Thue–Morse word is uniformly abelian-square-rich and that the function counting the number of distinct abelian-square factors of length 2n of the Thue–Morse word is 2-regular. As for Sturmian words, we prove that a Sturmian word sα of angle α is uniformly abelian-square-rich if and only if the irrational α has bounded partial quotients, that is, if and only if sα has bounded exponent
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