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2014 | 126 | 2 | 549-552

Article title

Letter Frequencies in the Kolakoski Sequence

Authors

Content

Title variants

Languages of publication

EN

Abstracts

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.

Keywords

EN

Year

Volume

126

Issue

2

Pages

549-552

Physical description

Dates

published
2014-08

Contributors

author
  • Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany

References

  • [1] R. Oldenburger, Trans. Am. Math. Soc. 46, 453 (1939), doi: 10.1090/S0002-9947-1939-0000352-9
  • [2] W. Kolakoski, Am. Math. Monthly 72, 674 (1965)
  • [3] W. Kolakoski, Am. Math. Monthly 73, 681 (1966)
  • [4] N.J.A. Sloane, The On-Line Encyclopedia of Integer Sequences, http://oeis.org
  • [5] C. Kimberling, http://faculty.evansville.edu/ck6/integer/index.html
  • [6] F.M. Dekking, 'Regularity and irregularity of sequences generated by automata', (exposé no. 9) Sém. Th. Nombres Bordeaux, 1979-1980, p. 901
  • [7] F.M. Dekking, 'On the structure of self generating sequences', (exposé no. 31), Sém. Th. Nombres Bordeaux, 1980-1981, p. 3101
  • [8] F.M. Dekking, The Mathematics of Long-Range Aperiodic Order, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 489, 115 (1997)
  • [9] B. Sing, More Kolakoski sequences, arXiv:1009.4061
  • [10] J. Nilsson, J. Integer Seq. 15, no. 6 (2012)
  • [11] M. Rao, http://www.arthy.org/kola/kola.php
  • [12] V. Chvátal, 'Notes on the Kolakoski sequence', DIMACS Technical Report 93-84 (1994) http://dimacs.rutgers.edu/techps/1993/93-84.ps
  • [13] K. Culik, II, J. Karhumäki, A. Lepistö, in: Lindenmayer Systems, Eds. G. Rozenberg, A. Salomaa, Springer, Berlin 1992, p. 93

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.bwnjournal-article-appv126n231kz
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