trureturingGitHub MATHEMATICAL ATLAS

Combinatorics / CONCEPT

Rank rigidity from a sharp chain bound

A colouring attaining the trivial monochromatic chain bound in an odd Boolean lattice is constant on each rank, and its ranks split equally between the two colours.

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DIRECT PREREQUISITES1
DIRECT CONSEQUENCES1
PROOF DEPTH1
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THEOREM

Equal-rank sets have equal colours

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Boolean sublattices and prefix chainsBoolean sublattices and prefixchainsRank rigidity from a sharp chain boundRank rigidity from a sharpchain boundThe odd-dimensional improvementThe odd-dimensional improvement
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Lean sourceResearch workspace
Status
Closed
Depth
1
Layer
D5/S3
Domain
Combinatorics
Node ID
D5/S3/Combinatorics/ErdosUlam/SublatticeRankRigidity
Repository path
D5/S3/Combinatorics/ErdosUlam/SublatticeRankRigidity.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
Source commit
b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
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37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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Dependency edges, status, and source coordinates come from the verified release and certified topology. Blueprint exposition is labeled separately. A fallback title carries no additional mathematical authority.