Logarithmic frequency in morphic sequences

Jason P. Bell[1]

  • [1] Department of Mathematics Simon Fraser University Burnaby, BC, V5A 1S6, CANADA

Journal de Théorie des Nombres de Bordeaux (2008)

  • Volume: 20, Issue: 2, page 227-241
  • ISSN: 1246-7405

Abstract

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We study the logarithmic frequency of letters and words in morphic sequences and show that this frequency must always exist, answering a question of Allouche and Shallit.

How to cite

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Bell, Jason P.. "Logarithmic frequency in morphic sequences." Journal de Théorie des Nombres de Bordeaux 20.2 (2008): 227-241. <http://eudml.org/doc/10834>.

@article{Bell2008,
abstract = {We study the logarithmic frequency of letters and words in morphic sequences and show that this frequency must always exist, answering a question of Allouche and Shallit.},
affiliation = {Department of Mathematics Simon Fraser University Burnaby, BC, V5A 1S6, CANADA},
author = {Bell, Jason P.},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Logarithmic frequency; morphic sequences; automatic sequences; Morphic sequence; logarithmic frequency},
language = {eng},
number = {2},
pages = {227-241},
publisher = {Université Bordeaux 1},
title = {Logarithmic frequency in morphic sequences},
url = {http://eudml.org/doc/10834},
volume = {20},
year = {2008},
}

TY - JOUR
AU - Bell, Jason P.
TI - Logarithmic frequency in morphic sequences
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2008
PB - Université Bordeaux 1
VL - 20
IS - 2
SP - 227
EP - 241
AB - We study the logarithmic frequency of letters and words in morphic sequences and show that this frequency must always exist, answering a question of Allouche and Shallit.
LA - eng
KW - Logarithmic frequency; morphic sequences; automatic sequences; Morphic sequence; logarithmic frequency
UR - http://eudml.org/doc/10834
ER -

References

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  1. J.-P. Allouche, J. Shallit, Automatic Sequences: Theory, Applications, Generalizations. Cambridge University Press, Cambridge, 2003. Zbl1086.11015MR1997038
  2. A. Cobham, Uniform tag sequences. Math. Systems Theory. 6 (1972), 164–192. Zbl0253.02029MR457011
  3. P. Michel, Sur les ensembles minimaux engendrés par les substitutions de longueur non constante. Thèse, Université de Rennes, 1975. 
  4. P. Michel, Stricte ergodicité dÕensembles minimaux de substitution. Théorie Ergodique: Actes des Journées Ergodiques, Rennes, 1973/1974, Lecture Notes in Mathematics 532, Springer-Verlag, 1976. Zbl0331.54036MR480942
  5. S. Nicolay, M. Rigo, About frequencies of letters in generalized automatic sequences. Theoret. Comput. Sci. 374 (2007), no. 1-3, 25–40. Zbl1162.68032MR2317465
  6. K. Saari, On the frequency of letters in morphic sequences. Computer science—theory and applications, 334–345, Lecture Notes in Comput. Sci. 3967, Springer, Berlin, 2006. Zbl1185.68398MR2261007
  7. K. Saari, On the frequency and periodicity of infinite words. PhD thesis, University of Turku, 2008. 

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