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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
The Pagoda Sequence: a Ramble through Linear Complexity, Number Walls, D0L Sequences, Finite State Automata, and Aperiodic Tilings
, 906
"... We review the concept of the number wall as an alternative to the traditional linear complexity profile (LCP), and sketch the relationship to other topics such as linear feedback shiftregister (LFSR) and contextfree Lindenmayer (D0L) sequences. A remarkable ternary analogue of the ThueMorse seque ..."
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We review the concept of the number wall as an alternative to the traditional linear complexity profile (LCP), and sketch the relationship to other topics such as linear feedback shiftregister (LFSR) and contextfree Lindenmayer (D0L) sequences. A remarkable ternary analogue of the ThueMorse
Rarified sums of the ThueMorse sequence
 Trans. Amer. Math. Soc
"... Abstract. Let q be an odd number and Sq,0(n) the difference between the number of k < n, k ≡ 0mod q, with an even binary digit sum and the corresponding number of k<n,k≡0mod q, with an odd binary digit sum. A remarkable theorem of Newman says that S3,0(n)> 0 for all n. Inthispaper it is pro ..."
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Cited by 7 (1 self)
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Abstract. Let q be an odd number and Sq,0(n) the difference between the number of k < n, k ≡ 0mod q, with an even binary digit sum and the corresponding number of k<n,k≡0mod q, with an odd binary digit sum. A remarkable theorem of Newman says that S3,0(n)> 0 for all n. Inthispaper it is proved that the same assertion holds if q is divisible by 3 or q =4 N +1. On the other hand, it is shown that the number of primes q ≤ x with this property is o(x / log x). Finally, analoga for “higher parities ” are provided. 1.
THE SINGULAR CONTINUOUS DIFFRACTION MEASURE OF THE THUEMORSE CHAIN
, 809
"... Abstract. The paradigm for singular continuous spectra in symbolic dynamics and in mathematical diffraction is provided by the ThueMorse chain, in its realisation as a binary sequence with values in {±1}. We revisit this example and derive a functional equation together with an explicit form of the ..."
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Cited by 14 (12 self)
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Abstract. The paradigm for singular continuous spectra in symbolic dynamics and in mathematical diffraction is provided by the ThueMorse chain, in its realisation as a binary sequence with values in {±1}. We revisit this example and derive a functional equation together with an explicit form
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
ThueMorse sequence and padic topology for the free monoid.
, 2000
"... Given two words u and v, the binomial coefficient u v is the number of ways v appears as a subword (or subsequence) of u. The ThueMorse sequence is the infinite word t = abbabaab obtained by iteration of the morphism (a) = ab and (b) = ba. We show that, for every prime p, and every positive int ..."
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Cited by 3 (2 self)
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Given two words u and v, the binomial coefficient u v is the number of ways v appears as a subword (or subsequence) of u. The ThueMorse sequence is the infinite word t = abbabaab obtained by iteration of the morphism (a) = ab and (b) = ba. We show that, for every prime p, and every positive
On the Delta Sequence of the ThueMorse Sequence
"... In this note, we investigate the delta sequence associated to the classical ThueMorse sequence and prove a conjecture about the delta sequence. Further, we generalize the ThueMorse sequence and show some results about this new sequence and its associated delta sequence. 1 ..."
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In this note, we investigate the delta sequence associated to the classical ThueMorse sequence and prove a conjecture about the delta sequence. Further, we generalize the ThueMorse sequence and show some results about this new sequence and its associated delta sequence. 1
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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Cited by 8 (0 self)
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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
On Sequence Entropy of ThueMorse Shift
"... Abstract. The paper summarizes properties of topological and sequence entropy of the Morse shift XM generated by the ThueMorse sequence tM. The first part is an estimation of growth rate of possible subwords in tM. We show a polynomial upper bound on the number of finite subwords occuring in tM wh ..."
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Abstract. The paper summarizes properties of topological and sequence entropy of the Morse shift XM generated by the ThueMorse sequence tM. The first part is an estimation of growth rate of possible subwords in tM. We show a polynomial upper bound on the number of finite subwords occuring in t
Repetitions of Words and the ThueMorse sequence
"... Introduction In his essay Notes on Structured Programming [2], Edsger Dijkstra uses as an example the problem of constructing a program that generates successively longer sequences of 0's, 1's, and 2's without nonempty, elementwise equal, adjoining subsequences, generating these ..."
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Introduction In his essay Notes on Structured Programming [2], Edsger Dijkstra uses as an example the problem of constructing a program that generates successively longer sequences of 0's, 1's, and 2's without nonempty, elementwise equal, adjoining subsequences, generating
Results 1  10
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188,694