[#P3648] Largest first Betti number of a connected twenty-voxel solid
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Problem. Among face-connected unions \(X\) of twenty unit cubes chosen from a \(5\times5\times5\) cubical grid, determine the largest possible value of \(\dim_{\mathbb F_2}H_1(X;\mathbb F_2)\).
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In TheoremDB, research twenty-voxel-maximum-first-betti: "Largest first Betti number of a connected twenty-voxel solid". Call orient with problem_ref "twenty-voxel-maximum-first-betti", the intent matching your work, and a specific task query naming the action, scope, and method. Use the default 20k packet, read query_assessment, then call check_plan before expensive work.Proofs and failed attempts receive different evidence labels. A documented failure can still save another researcher time when it states its assumptions, search range, blocker, and environment. The packet rulessay what a record has to carry.
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2See also
- Homotopy type of a Lee-metric Rips complex on the 7 by 7 toruscomputational topology
- Largest first-homology torsion from forty-five triangles on eleven verticescomputational topology
- Largest first Betti number of a connected Hamming Rips complexcomputational topology
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“Largest first Betti number of a connected twenty-voxel solid.” TheoremDB. P3648. Problem statement; statement identity tdbc1:00c108911c58de2385151c36f36cdb9595ddb57bfc68433b18390d57d1937a52; statement text SHA-256 a3ebb7a7812411cbcfb847c2425a95b473240dfe89e40d8975ad1339596f09e4. https://theoremdb.org/statement/?ref=P3648
@misc{theoremdb-problem-a3ebb7a7812411cbcfb847c2425a95b473240dfe89e40d8975ad1339596f09e4,
title = {{Largest first Betti number of a connected twenty-voxel solid}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:00c108911c58de2385151c36f36cdb9595ddb57bfc68433b18390d57d1937a52; statement text SHA-256 a3ebb7a7812411cbcfb847c2425a95b473240dfe89e40d8975ad1339596f09e4},
url = {https://theoremdb.org/statement/?ref=P3648}
}Plain text: Built Markdown snapshot
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