Entropy 2008, 10(4), 590-612; doi:10.3390/e10040590
Article

On the Entropy and Letter Frequencies of Powerfree Words

Uwe Grimm* email and Manuela Heueremail
Department of Mathematics&Statistics, The Open University, Walton Hall, Milton Keynes MK76AA, UK
* Author to whom correspondence should be addressed.
Received: 24 May 2008 / Accepted: 7 August 2008 / Published: 12 November 2008
(This article belongs to the Special Issue Concepts of Entropy and Their Applications - Papers presented at the Meeting at University of Melbourne, 26 November - 11 December 2007)
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Abstract: We review the recent progress in the investigation of powerfree words, with particular emphasis on binary cubefree and ternary squarefree words. Besides various bounds on the entropy, we provide bounds on letter frequencies and consider their empirical distribution obtained by an enumeration of binary cubefree words up to length 80.
Keywords: Entropy and information theory; symbolic sequences; combinatorics on words; integer sequences

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MDPI and ACS Style

Grimm, U.; Heuer, M. On the Entropy and Letter Frequencies of Powerfree Words. Entropy 2008, 10, 590-612.

AMA Style

Grimm U, Heuer M. On the Entropy and Letter Frequencies of Powerfree Words. Entropy. 2008; 10(4):590-612.

Chicago/Turabian Style

Grimm, Uwe; Heuer, Manuela. 2008. "On the Entropy and Letter Frequencies of Powerfree Words." Entropy 10, no. 4: 590-612.

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