Reproducible Code and Data for "Numerical Upper Bounds for Planar k-Fold Disk Coverings in Restricted Lattice and Two-Translate Families"
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| Format: | Recurso digital |
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Zenodo
2026
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| _version_ | 1866901712294379520 |
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| author | IM, YUNSEOP |
| author_facet | IM, YUNSEOP |
| contents | <p>This record provides the full reproduction package (code, scripts, and numerical outputs) for the study “Numerical Upper Bounds for Planar k-Fold Disk Coverings in Restricted Lattice and Two-Translate Families.”</p> <p>The package implements a deterministic grid-sampling estimator over a fundamental domain and a Lipschitz-based discretization correction to produce certified upper bounds on k-fold covering radii and induced density intervals. Experiments cover baseline lattices A2 and Z2 (D2 ≡ Z2 in 2D) for k ∈ {1,2,3}, as well as a two-translate family X = A2 ⊎ (A2 + t) with shift optimization at k = 2.</p> <p>Included are reproduction scripts, configuration files (grid resolution N, neighbor-box parameter M), validation diagnostics (coverage checks, neighbor completeness, grid refinement, shift invariance), and generated tables/figures corresponding to the manuscript (e.g., Table 1 and Figures 1–3).</p> <div> <div> </div> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18548751 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Reproducible Code and Data for "Numerical Upper Bounds for Planar k-Fold Disk Coverings in Restricted Lattice and Two-Translate Families" IM, YUNSEOP <p>This record provides the full reproduction package (code, scripts, and numerical outputs) for the study “Numerical Upper Bounds for Planar k-Fold Disk Coverings in Restricted Lattice and Two-Translate Families.”</p> <p>The package implements a deterministic grid-sampling estimator over a fundamental domain and a Lipschitz-based discretization correction to produce certified upper bounds on k-fold covering radii and induced density intervals. Experiments cover baseline lattices A2 and Z2 (D2 ≡ Z2 in 2D) for k ∈ {1,2,3}, as well as a two-translate family X = A2 ⊎ (A2 + t) with shift optimization at k = 2.</p> <p>Included are reproduction scripts, configuration files (grid resolution N, neighbor-box parameter M), validation diagnostics (coverage checks, neighbor completeness, grid refinement, shift invariance), and generated tables/figures corresponding to the manuscript (e.g., Table 1 and Figures 1–3).</p> <div> <div> </div> </div> |
| title | Reproducible Code and Data for "Numerical Upper Bounds for Planar k-Fold Disk Coverings in Restricted Lattice and Two-Translate Families" |
| url | https://doi.org/10.5281/zenodo.18548751 |