Characterizing switch-setting problems

Algebraic conditions and algorithmic procedures are given to determine whether an m × n rectangular configuration of switches can be transformed so that all switches are in the off position, regardless of initial configuration. However, when any switch is toggled, it and its rectilinearly adjacent n...

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Bibliographic Details
Published inLinear & multilinear algebra Vol. 43; no. 1-3; pp. 121 - 135
Main Authors Goldwasser, John, Klostermeyer, William, Trapp, George
Format Journal Article
LanguageEnglish
Published Gordon and Breach Science Publishers 01.01.1997
Subjects
AMS Subject Classification: 15A09, 05C99, 68Q25
Fibonacci polynomials
finite fields
grid graphs
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ISSN0308-1087
1563-5139
DOI10.1080/03081089708818520

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Summary:Algebraic conditions and algorithmic procedures are given to determine whether an m × n rectangular configuration of switches can be transformed so that all switches are in the off position, regardless of initial configuration. However, when any switch is toggled, it and its rectilinearly adjacent neighbors change state. Using linear algebra, a finite field representation of the problem, and an analysis of Fibonacci polynomials, conditions on m and n are given which characterize when the m × n problem can be solved.
ISSN:0308-1087
1563-5139
DOI:10.1080/03081089708818520