Linear numeration systems of order two
type: Item
instance of: scholarly article
title: Linear numeration systems of order two
zbMATH Open document ID: 0648.68066
DOI: 10.1016/0890-5401(88)90050-8
author: Christiane Frougny
published in: Information and Computation
publication date: 1988-01-01T00:00:00Z
review text: The author considers a numeration system \((U_ v,s)\) of the form \[ u_{n+2}=au_{n+1}+bu_ n,\quad u_ 0=1,\quad u_ 1=v\geq 2\quad. \] He shows that the system is complete only if \(v=a+1\) and \(s=a\). For the system \((U_{a+1},a)\) there exists a uniquely defined normal form of a word which may be computed by a composition of two subsequential machines. Addition of integers represented in \((U_{a+1},a)\) may be computed by a left-subsequential machine.
Mathematics Subject Classification ID: 68Q45
Mathematics Subject Classification ID: 11B37
Mathematics Subject Classification ID: 11A63
zbMATH DE Number: 4058874
zbMATH Keywords: numeration system
zbMATH Keywords: subsequential machines
reviewed by: M. A. Frumkin
MaRDI profile type: Publication
full work available at URL: 0890-5401(88)90050-8
OpenAlex ID: W1987087651
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description: scientific article; zbMATH DE number 4058874