Counting toroidal binary arrays
S. N. Ethier
TL;DR
This paper extends existing formulas to count toroidal binary arrays by including rotations and reflections of rows and columns, providing a more comprehensive enumeration method.
Contribution
It introduces a new formula for counting toroidal binary arrays considering both rotations and reflections of rows and columns, expanding prior work.
Findings
Derived a formula for counting arrays with rotations and reflections
Generalized previous formulas to include more symmetries
Provides a comprehensive enumeration method for toroidal arrays
Abstract
A formula for the number of toroidal m x n binary arrays, allowing rotation of the rows and/or the columns but not reflection, is known. Here we find a formula for the number of toroidal m x n binary arrays, allowing rotation and/or reflection of the rows and/or the columns.
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Taxonomy
Topicsgraph theory and CDMA systems · Cellular Automata and Applications