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Singleton Components at Ground Level

Abstract

Ground-level singleton components after the first component supply an additional statistic.

Definition 1.1 (Singleton components after the first).

Lean statement: D5/S3/Combinatorics/Nonnesting/NonnestingBasicRoyalGround.groundSingletons

Formalization. D5/S3/Combinatorics/Nonnesting/NonnestingBasicRoyalGround.groundSingletons (✓ 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.

Decompose a Dyck path into primitive components at ground level. Count the components consisting of a single upstep followed by a downstep, excluding the first component; the empty path has count zero.

References

  • Truth anchor: D5/S3/Combinatorics/Nonnesting/NonnestingBasicRoyalGround.groundSingletons