Enumeration of parallelograms in permutation matrices for improved bounds on the density of Costas arrays (Q259176)
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scientific article; zbMATH DE number 6554141
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Enumeration of parallelograms in permutation matrices for improved bounds on the density of Costas arrays |
scientific article; zbMATH DE number 6554141 |
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Enumeration of parallelograms in permutation matrices for improved bounds on the density of Costas arrays (English)
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11 March 2016
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Summary: A Costas array of order \(n\) is an \(n\times n\) permutation matrix such that all vectors between pairs of ones are distinct. Thus, a permutation matrix fails to be a Costas array if and only if it contains ones that form a (possibly degenerate) parallelogram. In this paper, we enumerate parallelograms in an \(n\times n\) permutation matrix. We use our new formulas to improve Davies's \(O(n^{-1})\) result for the density of Costas arrays.
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Costas array
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permutation
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enumeration
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