Toeplitz sequences, paperfolding, towers of Hanoi and progression-free sequences of integers
type: Item
instance of: scholarly article
title: Toeplitz sequences, paperfolding, towers of Hanoi and progression-free sequences of integers
zbMATH Open document ID: 0784.11008
author: Roland Bacher
author: Jean-Paul Allouche
published in: L'Enseignement Mathématique. 2e Série
publication date: 1993-06-29T00:00:00Z
review text: What is the relationship between folding a piece of paper, moving disks in the classical tower of Hanoi algorithm, and searching for maximal sequences of integers having no \(p\) terms in arithmetic progression? Well might one ask. The authors do, and answer their question by showing that the notion of Toeplitz sequence -- to wit an aperiodic sequence obtained by sequentially filling the `holes' in a periodic sequence by a periodic sequence, as introduced in \textit{K. Jacobs} and \textit{M. Keane} [Z. Wahrscheinlichkeitstheor. Verw. Geb. 13, 123-131 (1969; Zbl 0195.527)], allows a unified description of these matters. The authors' interesting remarks and the extensive list of references makes this a paper well worth study.
Mathematics Subject Classification ID: 11B85
zbMATH DE Number: 221266
zbMATH Keywords: tower of Hanoi algorithm
zbMATH Keywords: maximal sequences of integers having no \(p\) terms in arithmetic progression
zbMATH Keywords: Toeplitz sequence
zbMATH Keywords: aperiodic sequence
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 221266