trureturingGitHub MATHEMATICAL ATLAS

Combinatorics / CONCEPT

First letters at a fixed inversion number

For k<n, the mean first letter at inversion number k is M(n+1,k)/M(n,k).

Closed Authored exposition
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES0
PROOF DEPTH4
DOCUMENT LINKS0
THEOREM

The first-letter expectation identity

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Direct recorded relationships
List Inversions and Local Replacement BoundsList Inversions and LocalReplacement BoundsPanSkanderaWangAllSplitsWordPanSkanderaWangAllSplitsWordFirst letters at a fixed inversion numberFirst letters at a fixedinversion number
Proof dependencyStructural affinityDocument link

Certified topology / UPSTREAM

Prerequisites

Certified topology / DOWNSTREAM

Consequences

None recorded in this release.

RELATED KNOWLEDGE

Structural connections

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LIBRARY / RELEASE VERSIONS

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Certified provenance

Exact release coordinate

Lean sourceResearch workspace
Status
Closed
Depth
4
Layer
D5/S3
Domain
Combinatorics
Node ID
D5/S3/Combinatorics/Permutation/KageyInversionFirstLetter
Repository path
D5/S3/Combinatorics/Permutation/KageyInversionFirstLetter.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.