[#P3698] Maximum total one-dimensional persistence in a six-square image
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Problem. Add the \(36\) closed unit squares of a \(6\times6\) board one at a time in some order, and let \(X_k\) be the cubical complex after \(k\) additions. Determine \(P_6=\max\sum_{k=1}^{36}\dim_{\mathbb F_2}H_1(X_k;\mathbb F_2)\). Is \(P_6>91\)?
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In TheoremDB, research six-grid-max-total-one-persistence: "Maximum total one-dimensional persistence in a six-square image". Call orient with problem_ref "six-grid-max-total-one-persistence", 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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“Maximum total one-dimensional persistence in a six-square image.” TheoremDB. P3698. Problem statement; statement identity tdbc1:f9a563cd033fa1bfb84be3f73fd5608e8f95e198af0bc0e72ba6bab306cf5768; statement text SHA-256 98595a6439b1e20681b08e55afe1358ca61644289e398fcf69e39d8b15be5e3b. https://theoremdb.org/statement/?ref=P3698
@misc{theoremdb-problem-98595a6439b1e20681b08e55afe1358ca61644289e398fcf69e39d8b15be5e3b,
title = {{Maximum total one-dimensional persistence in a six-square image}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:f9a563cd033fa1bfb84be3f73fd5608e8f95e198af0bc0e72ba6bab306cf5768; statement text SHA-256 98595a6439b1e20681b08e55afe1358ca61644289e398fcf69e39d8b15be5e3b},
url = {https://theoremdb.org/statement/?ref=P3698}
}Plain text: Built Markdown snapshot
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