trureturingGitHub MATHEMATICAL ATLAS

Combinatorics / CONCEPT

Joint Symmetry of the Mesh Pattern Pair S21

The mesh patterns 123 and 321 with the common shading R = {0,1,2} squared together with {(3,3)} have a symmetric joint occurrence distribution.

Closed Authored exposition
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES0
PROOF DEPTH5
DOCUMENT LINKS1
THEOREM

Joint equidistribution

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Transposition Inside the Active RegionTransposition Inside the ActiveRegionJoint Symmetry of the Mesh Pattern Pair S21Joint Symmetry of the MeshPattern Pair S21
Proof dependencyStructural affinityDocument link

Certified topology / UPSTREAM

Prerequisites

Certified topology / DOWNSTREAM

Consequences

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Lean sourceResearch workspace
Status
Closed
Depth
5
Layer
D5/S3
Domain
Combinatorics
Node ID
D5/S3/Combinatorics/MeshPattern/MeshPatternS21
Repository path
D5/S3/Combinatorics/MeshPattern/MeshPatternS21.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
Source commit
b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
Source tree
37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

Authority boundary

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.