The Thue-Morse-Pascal double sequence and similar structures
type: Item
instance of: scholarly article
title: The Thue-Morse-Pascal double sequence and similar structures
zbMATH Open document ID: 1245.68152
author: Mihai Prunescu
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2011-10-21T00:00:00Z
review text: A recurrent two-dimensional sequence is a function \(a: \mathbb{N}^2 \to A\) with a finite alphabet \(A\) satisfying \(a(i,j) = f(a(i,j-1),a(i-1,j-1),a(i-1,j))\) for some function \(f: A^3 \to A\), for all \(i,j \in \mathbb{N}\). The sequences \(a(k,0)\) and \(a(0,k)\) are called initial conditions. The main theorem states that if a recurrent two-dimensional sequence with initial conditions defined by linear substitutions and a two-dimensional sequence that is generated by a certain type of planar substitutions are identical over a sufficiently large initial square, then they coincide everywhere. Some examples that can be automatically proven using a computer are given. All results are stated without proof in this note.
reviewed by: Wolfgang Steiner
Mathematics Subject Classification ID: 68R15
Mathematics Subject Classification ID: 11B37
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 5960867
zbMATH Keywords: planar substitution
zbMATH Keywords: recurrent sequence
MaRDI profile type: Publication
full work available at URL: j.crma.2011.07.022
OpenAlex ID: W2132941284
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DOI: 10.1016/J.CRMA.2011.07.022
description: scientific article; zbMATH DE number 5960867