trureturingGitHub MATHEMATICAL ATLAS

Combinatorics / CONCEPT

Necessary Gaps at Ascents

Avoidance of 1132 and 2213 restricts the gaps between consecutive downsteps at ascents.

Closed Authored exposition
DIRECT PREREQUISITES3
DIRECT CONSEQUENCES1
PROOF DEPTH6
DOCUMENT LINKS1
THEOREM

Necessity 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 Gaps
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Exact release coordinate

Lean sourceResearch workspace
Status
Closed
Depth
6
Layer
D5/S3
Domain
Combinatorics
Node ID
D5/S3/Combinatorics/Nonnesting/NonnestingRoyalLowGap
Repository path
D5/S3/Combinatorics/Nonnesting/NonnestingRoyalLowGap.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.