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Letter Frequencies in the Kolakoski Sequence

100%
Acta Physica Polonica A
|
2014
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vol. 126
|
issue 2
549-552
EN
The classical Kolakoski sequence is the unique sequence of two symbols {1,2}, starting with 1, which is equal to the sequence of lengths of consecutive segments of the same symbol (run lengths). We discuss here numerical aspects of the calculation of the letter frequencies and how to find bounds for these frequencies.
2
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Discrete Tomography: Magic Numbers for N-Fold Symmetry

51%
EN
We consider the problem of distinguishing convex subsets of n-cyclotomic model sets Λ by (discrete parallel) X-rays in prescribed Λ-directions. In this context, a 'magic number' m_{Λ} has the property that any two convex subsets of Λ can be distinguished by their X-rays in any set of m_{Λ} prescribed Λ-directions. Recent calculations suggest that (with one exception in the case n=4) the least possible magic number for n-cyclotomic model sets might just be N+1, where N=lcm(n,2).
EN
In the proofreading stage we overlooked a number of typographical errors. (On-line version is correct, this erratum applies to printed version only.)
4
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Scaling of the Thue-Morse Diffraction Measure

51%
EN
We revisit the well-known and much studied Riesz product representation of the Thue-Morse diffraction measure, which is also the maximal spectral measure for the corresponding dynamical spectrum in the complement of the pure point part. The known scaling relations are summarised, and some new findings are explained.
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