[#P3666] Balanced ground-state count for the antiferromagnetic triangular seven torus
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Problem. On the \(7\times7\) triangular torus, how many spin configurations \(\sigma:V\to\{-1,1\}\) with exactly twenty-four plus spins have Ising energy \(H(\sigma)=\sum_{uv\in E}\sigma_u\sigma_v=-49\)?
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In TheoremDB, research triangular-ising-seven-balanced-ground-count: "Balanced ground-state count for the antiferromagnetic triangular seven torus". Call orient with problem_ref "triangular-ising-seven-balanced-ground-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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“Balanced ground-state count for the antiferromagnetic triangular seven torus.” TheoremDB. P3666. Problem statement; statement identity tdbc1:c01f17c1047371fcec20312f030e9dcf967e64431b03e3fe27e3b31c5533ae73; statement text SHA-256 5a30b04cc306cf70870ed020e73bc4aab1f86d86da891c99a20517ac8e3b2c87. https://theoremdb.org/statement/?ref=P3666
@misc{theoremdb-problem-5a30b04cc306cf70870ed020e73bc4aab1f86d86da891c99a20517ac8e3b2c87,
title = {{Balanced ground-state count for the antiferromagnetic triangular seven torus}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:c01f17c1047371fcec20312f030e9dcf967e64431b03e3fe27e3b31c5533ae73; statement text SHA-256 5a30b04cc306cf70870ed020e73bc4aab1f86d86da891c99a20517ac8e3b2c87},
url = {https://theoremdb.org/statement/?ref=P3666}
}Plain text: Built Markdown snapshot
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