The linear system for Sudoku and a fractional completion threshold
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910412845350912 |
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| author | Dukes, Peter J. Nimegeers, Kate |
| author_facet | Dukes, Peter J. Nimegeers, Kate |
| contents | We study a system of linear equations associated with Sudoku latin squares. The coefficient matrix $M$ of the normal system has various symmetries arising from Sudoku. From this, we find the eigenvalues and eigenvectors of $M$, and compute a generalized inverse. Then, using linear perturbation methods, we obtain a fractional completion guarantee for sufficiently large and sparse rectangular-box Sudoku puzzles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_15279 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The linear system for Sudoku and a fractional completion threshold Dukes, Peter J. Nimegeers, Kate Combinatorics 05B15, 05C70 We study a system of linear equations associated with Sudoku latin squares. The coefficient matrix $M$ of the normal system has various symmetries arising from Sudoku. From this, we find the eigenvalues and eigenvectors of $M$, and compute a generalized inverse. Then, using linear perturbation methods, we obtain a fractional completion guarantee for sufficiently large and sparse rectangular-box Sudoku puzzles. |
| title | The linear system for Sudoku and a fractional completion threshold |
| topic | Combinatorics 05B15, 05C70 |
| url | https://arxiv.org/abs/2310.15279 |