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On the entropy and letter frequencies of ternary square-free words

Richard, Christoph and Grimm, Uwe (2004). On the entropy and letter frequencies of ternary square-free words. Electronic Journal of Combinatorics, 11(1) R14.

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Abstract

We enumerate all ternary length-1 square-free words, which are words avoiding squares of words up to length 1, for 1<=24. We analyse the singular behaviour of the corresponding generating functions. This leads to new upper entropy bounds for ternary square-free words. We then consider ternary square-free words with
fixed letter densities, thereby proving exponential growth for certain ensembles with various letter densities. We derive consequences for the free energy and entropy of
ternary square-free words.

Item Type: Journal Article
ISSN: 1077-8926
Extra Information: Preprint version math.CO/0302302 available from http://arxiv.org.abs.math.CO/0302302
Keywords: combinatorics on words; square-free words
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 5835
Depositing User: Users 13 not found.
Date Deposited: 09 Nov 2006
Last Modified: 05 Dec 2010 06:23
URI: http://oro.open.ac.uk/id/eprint/5835
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