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THE EHRENFEUCHTSILBERGER PROBLEM
, 2009
"... We consider repetitions in words and solve a longstanding open problem about the relation between the period and the length of its longest unbordered factor. A word u is called bordered if there exists a proper prefix that is also a suffix of u, otherwise it is called unbordered. In 1979 Ehrenfeuc ..."
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Ehrenfeucht and Silberger raised the following problem: What is the maximum length of a word w, w.r.t. the length τ of its longest unbordered factor still allowing that τ is shorter than the period π of w. We show that if w is longer than 7(τ − 1)/3 then τ = π which gives the optimal asymtotic bound.
On the Relation between Periodicity and Unbordered Factors of Finite Words
, 2008
"... Finite words and their overlap properties are considered in this paper. Let w be a finite word of length n with period p and where the maximum length of its unbordered factors equals k. A word is called unbordered if it possesses no proper prefix that is also a suffix of that word. Suppose k < p ..."
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property of maximum Duval extensions. Moreover, we show here that i < k/3, which in turn leads us to the solution of a special case of a problem raised by Ehrenfeucht and Silberger in 1979.
Periodicity and unbordered words: A proof of the extended Duval conjecture
 J. ACM
"... The relationship between the length of a word and the maximum length of its unbordered factors is investigated in this paper. Consider a finite word w of length n. We call a word bordered if it has a proper prefix which is also a suffix of that word. Let µ(w) denote the maximum length of all unborde ..."
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, in general, n ≥ 3µ(w) − 3 implies µ(w) = ∂(w) which gives an improved bound for the question raised by Ehrenfeucht and Silberger in 1979. 1
Periodicity and Unbordered Words A Proof of Duval’s Conjecture
"... Abstract. The relationship between the length of a word and the maximum length of its unbordered factors is investigated in this paper. A word is bordered, if it has a proper prefix that is also a suffix of that word. Consider a finite word w of length n. Let µ(w) denote the maximum length of its un ..."
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(w) = ∂(w) which gives an improved bound for the question asked by Ehrenfeucht and Silberger in 1979. 1
Periodicity and Unbordered Words: A proof of the . . .
, 2003
"... The relationship between the length of a word and the maximum length of its unbordered factors is investigated in this paper. Consider a finite word w of length n. We call a word bordered, if it has a proper prefix which is also a suffix of that word. Let µ(w) denote the maximum length of all unbord ..."
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, in general, n ≥ 3µ(w) − 2 implies µ(w) = ∂(w) which gives an improved bound for the question asked by Ehrenfeucht and Silberger in 1979.
DOI: 10.4171/OWR/2010/37 MiniWorkshop: Combinatorics on Words
, 2010
"... Abstract. The area of combinatorics on words is concerned with properties of sequences of symbols. It is characteristic to the field that questions arise from various mathematical problems, and hence, many fundamental results on words have been established in different areas. Over the last two decad ..."
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Abstract. The area of combinatorics on words is concerned with properties of sequences of symbols. It is characteristic to the field that questions arise from various mathematical problems, and hence, many fundamental results on words have been established in different areas. Over the last two
Periodicity and Unbordered Segments of Words
"... We shall give an introduction to the problem area concerning the well known Duval’s conjecture, which was announced to be solved in [12]. 1 ..."
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We shall give an introduction to the problem area concerning the well known Duval’s conjecture, which was announced to be solved in [12]. 1
Results 1  10
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