Corpus ID: 16114176

THE MATHEMATICS OF PER NØRGÅRD ’ S RHYTHMIC INFINITY SYSTEM

@inproceedings{Shallit2002THEMO,
  title={THE MATHEMATICS OF PER N{\O}RG{\AA}RD ’ S RHYTHMIC INFINITY SYSTEM},
  author={Jeffrey Shallit},
  year={2002}
}
The Danish composer Per Nørg̊ard (1932–) invented a procedure for generating rhythms which was described by Erling Kullberg [5]. Reworded in mathematical notation, this procedure is as follows: Let the Fibonacci numbers (Fn)n≥0 be defined as usual by F0 = 0, F1 = 1, and Fn = Fn−1 + Fn−2. Starting with the pair (c0, c1) = (F2n, F2n+1), perform the following operation n− 2 times: • If a number Fi appears in an even-indexed position, replace it with (Fi−2, Fi−1) • If a number Fi appears in an odd… Expand

Figures from this paper

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By Zeckendorf’s theorem, an equivalent definition of the Fibonacci sequence (appropriately normalized) is that it is the unique sequence of increasing integers such that every positive number can beExpand
Volume Index
ALLADI, KRISHNASWAMI. "A Farey Sequence of Fibonacci Numbers," Vol. 13, No. 1, pp. 1-10. "A Rapid Method to Form Farey Fibonacci Fractions," Vol. 13, No. 1,p. 31. "Generalized Fibonacci Tiling," Vol.Expand
The ring of k-regular sequences, II
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This paper proves some new results, gives many new examples from the literature, and state some open problems in the study of k-regular sequences. Expand
N T ] 8 J un 2 02 0 On three conjectures of
We prove three conjectures, related to the paperfolding sequence, in a recent paper of P. Barry.
On some conjectures of P. Barry
We prove a number of conjectures [arXiv:2005.04066] recently stated by P. Barry, related to the paperfolding sequence and the Rueppel sequence.

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AMS Classification Numbers: 11B39, 68Q45
  • AMS Classification Numbers: 11B39, 68Q45