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Connectivity Constraints

Abstract

Connectivity of the joined half matchings excludes incompatible endpoint patterns.

Theorem 1.1 (Connected endpoint cases).

Lean statement: D5/S3/Combinatorics/SemiMeanderSecondDiagonal/Stage3.connected_endpoint_cases

Proof. Machine-checked in Lean as D5/S3/Combinatorics/SemiMeanderSecondDiagonal/Stage3.connected_endpoint_cases (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. Hunter Hogan (2026). OEIS A400429, semi-meanders by crossings and winding number. URL: https://oeis.org/A400429.

Commentary.

A connected joined matching has only the endpoint configurations admitted by the local pairing classification.

References