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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
The irreducibility of the space of curves of given genus
 Publ. Math. IHES
, 1969
"... Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k ~ ..."
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Cited by 512 (2 self)
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~ (1, and then the result is classical. A simple proof appears in EnriquesChisini [E, vol. 3, chap. 3], based on analyzing the totality of coverings of p1 of degree n, with a fixed number d of ordinary branch points. This method has been extended to char. p by William Fulton [F], using specializations
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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Cited by 3 (0 self)
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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
The ThueMorse sequence along squares is normal, manuscript
"... Abstract. The ThueMorse sequence is a classical example of an almost periodic (or uniformly recurrent) sequence in the sense that its associated symbolic dynamical system is minimal. We prove that the subsequence along squares of the ThueMorse sequence is normal. 1. ..."
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Cited by 1 (1 self)
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Abstract. The ThueMorse sequence is a classical example of an almost periodic (or uniformly recurrent) sequence in the sense that its associated symbolic dynamical system is minimal. We prove that the subsequence along squares of the ThueMorse sequence is normal. 1.
A Symmetry Group of a ThueMorse Quasicrystal
, 2008
"... 1 Abstract. We present a method of coding general selfsimilar structures. In particular, we construct a symmetry group of a onedimensional ThueMorse quasicrystal, i.e., of a nonperiodic ground state of a certain translationinvariant, exponentially decaying interaction. A symmetry group of a thre ..."
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1 Abstract. We present a method of coding general selfsimilar structures. In particular, we construct a symmetry group of a onedimensional ThueMorse quasicrystal, i.e., of a nonperiodic ground state of a certain translationinvariant, exponentially decaying interaction. A symmetry group of a
Integral Geometry and Real Zeros of ThueMorse Polynomials
, 2000
"... We study the average number of intersecting points of a given curve with random hyperplanes in an ndimensional Euclidean space. As noticed by A. Edelman and E. Kostlan this problem is closely linked to finding the average number of real zeros of random polynomials. They show that a real polynomial ..."
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Cited by 2 (2 self)
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+ ff nX . Theoretical results are given for the ThueMorse polynomials as well as numerical evidence for other polynomials.
Results 1  10
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825,220