Adjacent Downstep Pairs

Abstract

Consecutive downsteps give a local statistic on step sequences.

Definition 1.1 (Adjacent downstep count).

Lean statement: D5/S3/Combinatorics/Nonnesting/NonnestingBasicRoyalDownRuns.downPairs

Formalization. D5/S3/Combinatorics/Nonnesting/NonnestingBasicRoyalDownRuns.downPairs (✓ 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.

Count the adjacent pairs of downsteps in a step sequence, including overlapping pairs within a run of downsteps.

References

• Truth anchor: D5/S3/Combinatorics/Nonnesting/NonnestingBasicRoyalDownRuns.downPairs