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Words avoiding 7powers and the ThueMorse morphism
 Internat. J. Found. Comput. Sci
"... In 1982, Séébold showed that the only overlapfree binary words that are the fixed points of nonidentity morphisms are the ThueMorse word and its complement. We show that the same result holds if the term ‘overlapfree ’ is replaced with ‘ 7 3powerfree’. Furthermore, the number 7 3 ..."
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In 1982, Séébold showed that the only overlapfree binary words that are the fixed points of nonidentity morphisms are the ThueMorse word and its complement. We show that the same result holds if the term ‘overlapfree ’ is replaced with ‘ 7 3powerfree’. Furthermore, the number 7 3
The ThueMorse sequence
, 2010
"... We consider compact group generalizations T(n) of the ThueMorse sequence and prove that the subsequence T(n 2) is uniformly distributed with respect to a measure ν that is absolutely continuous with respect to the Haar measure. The proof is based on a proper generalization of the Fourier based meth ..."
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We consider compact group generalizations T(n) of the ThueMorse sequence and prove that the subsequence T(n 2) is uniformly distributed with respect to a measure ν that is absolutely continuous with respect to the Haar measure. The proof is based on a proper generalization of the Fourier based
On the critical exponent of generalized ThueMorse words ∗
, 2007
"... For certain generalized ThueMorse words t, we compute the critical exponent, i.e., the supremum of the set of rational numbers that are exponents of powers in t, and determine exactly the occurrences of powers realizing it. Keywords: ThueMorse; critical exponent; occurrences. MSC (2000): 68R15; 11 ..."
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For certain generalized ThueMorse words t, we compute the critical exponent, i.e., the supremum of the set of rational numbers that are exponents of powers in t, and determine exactly the occurrences of powers realizing it. Keywords: ThueMorse; critical exponent; occurrences. MSC (2000): 68R15
On the Critical Exponent of Generalized ThueMorse Words
, 2007
"... For certain generalized ThueMorse words t, we compute the critical exponent, i.e., the supremum of the set of rational numbers that are exponents of powers in t, and determine exactly the occurrences of powers realizing it. ..."
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For certain generalized ThueMorse words t, we compute the critical exponent, i.e., the supremum of the set of rational numbers that are exponents of powers in t, and determine exactly the occurrences of powers realizing it.
An analogue of the ThueMorse sequence
"... We consider the finite binary words Z(n), n ∈ N, defined by the following selfsimilar process: Z(0): = 0, Z(1): = 01, and Z(n + 1): = Z(n) · Z(n − 1), where the dot · denotes word concatenation, and w the word obtained from w by exchanging the zeros and the ones. Denote by Z(∞) = 01110100... the l ..."
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... the limiting word of this process, and by z(n) the n’th bit of this word. This sequence z is an analogue of the ThueMorse sequence. We show that a theorem of Bacher and Chapman relating the latter to a “Sierpiński matrix ” has a natural analogue involving z. The semiinfinite selfsimilar matrix which plays
On the 2abelian Complexity of Thue–Morse
, 2014
"... We show that the 2abelian complexity of the infinite Thue–Morse word is 2regular, and other properties of the 2abelian complexity. We also show sharp bounds for the length of unique extensions of Thue–Morse words of size n. 1 ..."
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We show that the 2abelian complexity of the infinite Thue–Morse word is 2regular, and other properties of the 2abelian complexity. We also show sharp bounds for the length of unique extensions of Thue–Morse words of size n. 1
Lyndon factorization of the ThueMorse word and its relatives
, 1997
"... this paper, we concentrate on the ThueMorse word and give the computation of its Lyndon factorization (Theorem 3.1) and describe some of its properties (Corollary 3.2, Remark 3.3 and Corollary 3.4). Incidentally, we are able to compute the factorization for the `dual' ThueMorse word in whic ..."
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this paper, we concentrate on the ThueMorse word and give the computation of its Lyndon factorization (Theorem 3.1) and describe some of its properties (Corollary 3.2, Remark 3.3 and Corollary 3.4). Incidentally, we are able to compute the factorization for the `dual' ThueMorse word
A relative of the ThueMorse Sequence
 Discrete Math
, 1999
"... We study a sequence, c, which encodes the lengths of blocks in the ThueMorse sequence. In particular, we show that the generating function for c is a simple product. Consider the sequence c : c 0 ; c 1 ; c 2 ; c 3 ; : : : = 1; 3; 4; 5; 7; 9; 11; 12; 13; : : : defined to be the lexicographically ..."
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We study a sequence, c, which encodes the lengths of blocks in the ThueMorse sequence. In particular, we show that the generating function for c is a simple product. Consider the sequence c : c 0 ; c 1 ; c 2 ; c 3 ; : : : = 1; 3; 4; 5; 7; 9; 11; 12; 13; : : : defined to be the lexicographically
Univoque numbers and an avatar of ThueMorse
"... Univoque numbers are real numbers λ> 1 such that the number 1 admits a unique expansion in base λ, i.e., a unique expansion 1 = ∑ j≥0 ajλ−(j+1) , with aj ∈ {0,1,..., ⌈λ ⌉ − 1} for every j ≥ 0. A variation of this definition was studied in 2002 by Komornik and Loreti, together with sequences call ..."
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positive integer. We also prove that this last number is transcendental. An avatar of the ThueMorse sequence, namely the fixed point beginning in 3 of the morphism 3 → 31, 2 → 30, 1 → 03, 0 → 02, occurs in a “universal ” manner.
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