On the Entropy and Letter Frequencies of Ternary Square-Free Words
Combinatorics
2007-05-23 v2 Mathematical Physics
math.MP
Abstract
We enumerate all ternary length-l square-free words, which are words avoiding squares of words up to length l, for l<=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.
Keywords
Cite
@article{arxiv.math/0302302,
title = {On the Entropy and Letter Frequencies of Ternary Square-Free Words},
author = {Christoph Richard and Uwe Grimm},
journal= {arXiv preprint arXiv:math/0302302},
year = {2007}
}
Comments
17 pages, 2 figures