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The Height of a Weak Ascent Sequence

Abstract

The weak ascent count bounds every entry of a weak ascent sequence.

Theorem 1.1 (The maximum lies below the height).

Lean statement: D5/S3/Combinatorics/WeakAscent/WeakAscentGrowth.height_dominates

Proof. Machine-checked in Lean as D5/S3/Combinatorics/WeakAscent/WeakAscentGrowth.height_dominates (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. Beáta Bényi, Toufik Mansour, José L. Ramírez (2024). Pattern Avoidance in Weak Ascent Sequences. DOI: 10.46298/dmtcs.12273. URL: https://arxiv.org/abs/2309.06518v4.

Commentary.

For every weak ascent sequence, its maximum entry is strictly less than one plus its weak ascent count, taking the maximum of the empty sequence as zero.

References