Some properties of periodic words
type: Item
instance of: scholarly article
title: Some properties of periodic words
zbMATH Open document ID: 1023.68072
DOI: 10.1023/A:1020539118744
published in: Mathematical Notes
publication date: 2003-06-15T00:00:00Z
review text: It is shown that if \(T\) is a simple (i.e., primitive) word such that \(T^3=XY\) for some words \(X\) and \(Y\), then \(X\) or \(Y\) has the same minimum period as \(T\) does. The proof uses elementary combinatorial arguments on words, and it can be simplified by considering Lyndon words. Indeed, \(T^3=Z_1L^2Z_2\), where \(L\) is a Lyndon word conjugate to \(T\). Hence \(T^3=XY\) implies that either \(X\) or \(Y\) contains \(L\) as a factor. The claim follows from this, since the minimum period of \(L\) is its length. A similar result is proven for the case \(T^2=XY\) (with \(T\) simple).
reviewed by: Tero Harju
Mathematics Subject Classification ID: 68R15
Mathematics Subject Classification ID: 20M05
zbMATH DE Number: 1928290
zbMATH Keywords: periodic words
zbMATH Keywords: semigroups
zbMATH Keywords: equations
zbMATH Keywords: simple words
zbMATH Keywords: Lyndon words
author: Victor S. Guba
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1928290