Balanced words
type: Item
instance of: scholarly article
title: Balanced words
zbMATH Open document ID: 1070.68129
author: L. Vuillon
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2005-06-09T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bbms/1074791332
review text: A finite or infinite word defined over a finite alphabet \({\mathcal A}\) is said to be balanced if, for any pair of factors \((W,W')\) with the same length and any element \(a\) in \({\mathcal A}\), we have \[ \left| | W|_a-| W'|_a\right|\leq 1. \] Here \(| W|_a\) denotes the number of occurrences of the letter \(a\) in the word \(W\). The paper under review presents an interesting survey of the notion of balance. Classical results are recalled, but the purpose of the author is mainly to focus on various generalizations of this notion with applications and with open problems in number theory, theoretical computer science or ergodic theory. Most of the mentioned results correspond to recent works.
reviewed by: Boris Adamczewski
Mathematics Subject Classification ID: 68R15
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 37B10
zbMATH DE Number: 2174595
zbMATH Keywords: combinatorics on words
zbMATH Keywords: balance property
zbMATH Keywords: Sturmian words
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2174595