On the entropy and letter frequencies of powerfree words
Uwe Grimm, Manuela Heuer
TL;DR
This paper reviews recent advances in understanding powerfree words, focusing on entropy bounds, letter frequency distributions, and empirical data from enumerations of binary cubefree words up to length 80.
Contribution
It provides new bounds on entropy and letter frequencies for powerfree words, including empirical data from enumeration.
Findings
Bounds on entropy for powerfree words
Letter frequency distributions in binary cubefree words
Empirical enumeration up to length 80
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.
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