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Combined Dyck Weights

Abstract

Adjacent downsteps and later singleton components contribute to the same weight.

Definition 1.1 (Combined weight sum).

Lean statement: D5/S3/Combinatorics/Nonnesting/NonnestingBasicRoyalGroundCount.groundWeight

Formalization. D5/S3/Combinatorics/Nonnesting/NonnestingBasicRoyalGroundCount.groundWeight (✓ std3).

Source. Repository-derived.

Acknowledgement. Sergi Elizalde, Amya Luo (2024). Pattern avoidance in nonnesting permutations. DOI: 10.48550/arXiv.2412.00336. URL: https://arxiv.org/abs/2412.00336v6.

Commentary.

For semilength n, sum over all Dyck paths two to the power of the number of adjacent downstep pairs plus the number of ground-level singleton components after the first component.

References