trureturingGitHub MATHEMATICAL ATLAS

Combinatorics / CONCEPT

Avoidance from Permitted Gaps

The increasing-block order and permitted Dyck gaps imply avoidance of 1132 and 2213.

Closed Authored exposition
DIRECT PREREQUISITES4
DIRECT CONSEQUENCES1
PROOF DEPTH7
DOCUMENT LINKS1
THEOREM

Sufficiency of the gap condition

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Permutation and Dyck-Path EncodingPermutation and Dyck-PathEncodingSeparation at DescentsSeparation at DescentsDyck Shape of a Doubled WordDyck Shape of a Doubled WordNecessary Gaps at AscentsNecessary Gaps at AscentsAvoidance from Permitted GapsAvoidance from Permitted GapsCompositions for a Fixed Dyck ShapeCompositions for a Fixed DyckShape
Proof dependencyStructural affinityDocument link

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Exact release coordinate

Lean sourceResearch workspace
Status
Closed
Depth
7
Layer
D5/S3
Domain
Combinatorics
Node ID
D5/S3/Combinatorics/Nonnesting/NonnestingRoyalLowConverse
Repository path
D5/S3/Combinatorics/Nonnesting/NonnestingRoyalLowConverse.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
Source commit
b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
Source tree
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.