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Displaying similar documents to “Hankel determinants of the Thue-Morse sequence”

Squares and overlaps in the Thue-Morse sequence and some variants

Shandy Brown, Narad Rampersad, Jeffrey Shallit, Troy Vasiga (2006)

RAIRO - Theoretical Informatics and Applications

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We consider the position and number of occurrences of squares in the Thue-Morse sequence, and show that the corresponding sequences are -regular. We also prove that changing any finite but nonzero number of bits in the Thue-Morse sequence creates an overlap, and any linear subsequence of the Thue-Morse sequence (except those corresponding to decimation by a power of ) contains an overlap.

Number Sequences in an Integral Form with a Generalized Convolution Property and Somos-4 Hankel Determinants

Rajkovic, Predrag M., Barry, Paul, Savic, Natasa (2012)

Mathematica Balkanica New Series

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MSC 2010: 11B83, 05A19, 33C45 This paper is dealing with the Hankel determinants of the special number sequences given in an integral form. We show that these sequences satisfy a generalized convolution property and the Hankel determinants have the generalized Somos-4 property. Here, we recognize well known number sequences such as: the Fibonacci, Catalan, Motzkin and SchrÄoder sequences, like special cases.

Some new examples of recurrence and non-recurrence sets for products of rotations on the unit circle

Sophie Grivaux, Maria Roginskaya (2013)

Czechoslovak Mathematical Journal

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We study recurrence and non-recurrence sets for dynamical systems on compact spaces, in particular for products of rotations on the unit circle 𝕋 . A set of integers is called r -Bohr if it is recurrent for all products of r rotations on 𝕋 , and Bohr if it is recurrent for all products of rotations on 𝕋 . It is a result due to Katznelson that for each r ≥ 1 there exist sets of integers which are r -Bohr but not ( r + 1 ) -Bohr. We present new examples of r -Bohr sets which are not Bohr, thanks to a construction...