A Gale-Berlekamp permutation-switching problem in higher dimensions
Let an $n\times n$ array $\left( a_{ij}\right) $ of lights be given, each either on (when $a_{ij}=1$) or off (when $a_{ij}=-1$). For each row and each column there is a switch so that if the switch is pulled ($x_{i}=-1$ for row $i$ and $y_{j}=-1$ for column $j$) all of the lights in that line are sw...
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Main Authors | , |
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Format | Journal Article |
Language | English |
Published |
28.01.2018
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Subjects | |
Online Access | Get full text |
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Summary: | Let an $n\times n$ array $\left( a_{ij}\right) $ of lights be given, each
either on (when $a_{ij}=1$) or off (when $a_{ij}=-1$). For each row and each
column there is a switch so that if the switch is pulled ($x_{i}=-1$ for row
$i$ and $y_{j}=-1$ for column $j$) all of the lights in that line are switched:
on to off or off to on. The unbalancing lights problem (Gale-Berlekamp
switching game) consists in maximizing the difference between the lights on and
off. We obtain the exact parameters for a generalization of the unbalancing
lights problem in higher dimensions. |
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DOI: | 10.48550/arxiv.1801.09194 |