trureturingGitHub MATHEMATICAL ATLAS

Combinatorics / CONCEPT

Factorizations at the Initial Ascent and Final Descent

Lists of Dyck paths factor a Dyck path at its initial ascent or final descent.

Closed Authored exposition
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES3
PROOF DEPTH5
DOCUMENT LINKS1
THEOREM

Two bijective run factorizations

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Direct recorded relationships
Reflection of Dyck PathsReflection of Dyck PathsFactorizations at the Initial Ascent and Final DescentFactorizations at the InitialAscent and Final DescentGenerating Function for the Final DescentGenerating Function for theFinal DescentGenerating Function for a Marked Interior DescentGenerating Function for aMarked Interior DescentGenerating Function for the Penultimate DescentGenerating Function for thePenultimate Descent
Proof dependencyStructural affinityDocument link

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Certified provenance

Exact release coordinate

Lean sourceResearch workspace
Status
Closed
Depth
5
Layer
D5/S3
Domain
Combinatorics
Node ID
D5/S3/Combinatorics/InversionSeq/InversionSeq152Factor
Repository path
D5/S3/Combinatorics/InversionSeq/InversionSeq152Factor.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.