Counting partial Hadamard matrices in the cubic regime
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915903357059072 |
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| author | Davis, Damek |
| author_facet | Davis, Damek |
| contents | We give a precise asymptotic formula for the number of $n\times 4t$ partial Hadamard matrices in the regimes $t/n^3\to\infty$ and $t/n^3\toΘ$ for sufficiently large fixed $Θ$. This strengthens earlier results of de~Launey and Levin, who obtained the asymptotic for $t/n^{12}\to\infty$, and of Canfield, who extended this to $t/n^4\to\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_30013 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Counting partial Hadamard matrices in the cubic regime Davis, Damek Probability Combinatorics We give a precise asymptotic formula for the number of $n\times 4t$ partial Hadamard matrices in the regimes $t/n^3\to\infty$ and $t/n^3\toΘ$ for sufficiently large fixed $Θ$. This strengthens earlier results of de~Launey and Levin, who obtained the asymptotic for $t/n^{12}\to\infty$, and of Canfield, who extended this to $t/n^4\to\infty$. |
| title | Counting partial Hadamard matrices in the cubic regime |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2603.30013 |