vix.ing · top · new · best · stats · spec

On the Entropy and Letter Frequencies of Powerfree Words

2008/11/12 by Uwe Grimm, Manuela Heuer
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Binary data #Binary entropy function #Binary number #Coding theory and cryptography #Entropy (arrow of time) #Enumeration #Information theory #Square-free integer #Ternary operation #math.CO #semigroups and automata theory

paper · pdf · doi:10.3390/e10040590

published as Entropy 10 (2008), 590-612 · 19 pages, 4 figures

openalex publication_date 2008/11/12 · arxiv created 2008/11/13 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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.

Citations