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Palindrome complexity
 To appear, Theoret. Comput. Sci
, 2002
"... We study the palindrome complexity of infinite sequences on finite alphabets, i.e., the number of palindromic factors (blocks) of given length occurring in a given sequence. We survey the known results and obtain new results for some sequences, in particular for Rote sequences and for fixed points o ..."
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Cited by 17 (2 self)
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We study the palindrome complexity of infinite sequences on finite alphabets, i.e., the number of palindromic factors (blocks) of given length occurring in a given sequence. We survey the known results and obtain new results for some sequences, in particular for Rote sequences and for fixed points
Palindromes in infinite ternary words
, 2009
"... We study infinite words u over an alphabet A satisfying the property P: P(n) + P(n + 1) = 1 + #A for any n ∈ N, where P(n) denotes the number of palindromic factors of length n occurring in the language of u. We study also infinite words satisfying a stronger property PE: every palindrome of u has ..."
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Cited by 1 (1 self)
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We study infinite words u over an alphabet A satisfying the property P: P(n) + P(n + 1) = 1 + #A for any n ∈ N, where P(n) denotes the number of palindromic factors of length n occurring in the language of u. We study also infinite words satisfying a stronger property PE: every palindrome of u has
Palindromic richness
 Eur. J. Comb
"... In this paper, we study combinatorial and structural properties of a new class of finite and infinite words that are ‘rich ’ in palindromes in the utmost sense. A characteristic property of socalled rich words is that all complete returns to any palindromic factor are themselves palindromes. These ..."
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Cited by 15 (2 self)
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In this paper, we study combinatorial and structural properties of a new class of finite and infinite words that are ‘rich ’ in palindromes in the utmost sense. A characteristic property of socalled rich words is that all complete returns to any palindromic factor are themselves palindromes
PALINDROMIC PRIMITIVES AND PALINDROMIC BASES IN THE FREE GROUP OF RANK TWO
, 2005
"... Abstract. The present paper records more details of the relationship between primitive elements and palindromes in F2, the free group of rank two. We characterise the conjugacy classes of primitive elements which contain palindromes as those which contain cyclically reduced words of odd length. We i ..."
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Cited by 8 (0 self)
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Abstract. The present paper records more details of the relationship between primitive elements and palindromes in F2, the free group of rank two. We characterise the conjugacy classes of primitive elements which contain palindromes as those which contain cyclically reduced words of odd length. We
Palindrome Complexity Bounds For Primitive Substitution Sequences
, 2000
"... We consider onesided infinite words generated via iteration by primitive substitutions on finite alphabets and provide bounds on the palindrome complexity function as well as uniform bounds on the frequencies of palindromes in such words. As an application of these bounds, we prove that the str ..."
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Cited by 15 (7 self)
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We consider onesided infinite words generated via iteration by primitive substitutions on finite alphabets and provide bounds on the palindrome complexity function as well as uniform bounds on the frequencies of palindromes in such words. As an application of these bounds, we prove
ENUMERATING PALINDROMES AND PRIMITIVES IN RANK TWO FREE GROUPS
, 2009
"... Let F = 〈a, b 〉 be a rank two free group. A word W(a, b) in F is primitive if it, along with another group element, generates the group. It is a palindrome (with respect to a and b) if it reads the same forwards and backwards. It is known that in a rank two free group any primitive element is conju ..."
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Cited by 7 (3 self)
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Let F = 〈a, b 〉 be a rank two free group. A word W(a, b) in F is primitive if it, along with another group element, generates the group. It is a palindrome (with respect to a and b) if it reads the same forwards and backwards. It is known that in a rank two free group any primitive element
On minimal factorizations of words as products of palindromes
, 2014
"... Given a finite word u, we define its palindromic length upal to be the least number n such that u = v1v2... vn with each vi a palindrome. We address the following open question: Does there exist an infinite non ultimately periodic word w and a positive integer P such that upal ≤ P for each facto ..."
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Given a finite word u, we define its palindromic length upal to be the least number n such that u = v1v2... vn with each vi a palindrome. We address the following open question: Does there exist an infinite non ultimately periodic word w and a positive integer P such that upal ≤ P for each
Palindrome prefixes and Episturmian words
, 2008
"... Let w be an infinite word on an alphabet A. We denote by (ni)i≥1 the increasing sequence (assumed to be infinite) of all lengths of palindrome prefixes of w. In this text, we give an explicit construction of all words w such that ni+1 ≤ 2ni + 1 for all i, and study these words. Special examples inc ..."
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Cited by 20 (0 self)
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Let w be an infinite word on an alphabet A. We denote by (ni)i≥1 the increasing sequence (assumed to be infinite) of all lengths of palindrome prefixes of w. In this text, we give an explicit construction of all words w such that ni+1 ≤ 2ni + 1 for all i, and study these words. Special examples
Results 1  10
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