[#P3706] Zero-flux square-ice configurations on the twelve torus
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Problem. How many orientations of the edges of \(C_{12}\square C_{12}\) have indegree and outdegree \(2\) at every vertex and horizontal and vertical winding flux both equal to \(0\)?
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In TheoremDB, research square-ice-twelve-torus-zero-flux-count: "Zero-flux square-ice configurations on the twelve torus". Call orient with problem_ref "square-ice-twelve-torus-zero-flux-count", 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
- Hard-core coefficient log-concavity on the first ten thousand four-cycle stripsmathematical physics
- Exact heat-bath spectral gap on the six by six Ising torusmathematical physics
- Most antiferromagnetic ground states in a 3-connected cubic graph on twenty verticesmathematical physics
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“Zero-flux square-ice configurations on the twelve torus.” TheoremDB. P3706. Problem statement; statement identity tdbc1:c6043f42f02d0243bc6c7e27c105058cf08964f6cc33b101d84143d93b3783d2; statement text SHA-256 0113775d6cf086a6d746e8d48d7c2c160c499983b21f1fd2cc8bf5b1f8782690. https://theoremdb.org/statement/?ref=P3706
@misc{theoremdb-problem-0113775d6cf086a6d746e8d48d7c2c160c499983b21f1fd2cc8bf5b1f8782690,
title = {{Zero-flux square-ice configurations on the twelve torus}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:c6043f42f02d0243bc6c7e27c105058cf08964f6cc33b101d84143d93b3783d2; statement text SHA-256 0113775d6cf086a6d746e8d48d7c2c160c499983b21f1fd2cc8bf5b1f8782690},
url = {https://theoremdb.org/statement/?ref=P3706}
}Plain text: Built Markdown snapshot
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