Keyboard shortcuts

Press ← or → to navigate between chapters

Press ? to show this help

Press Esc to hide this help

Counting Words in the Second Class

Abstract

The target series counts words in the second Class 215 avoidance family.

Theorem 1.1 (Word counts as target coefficients).

Lean statement: D5/S3/Combinatorics/WeakAscent/WeakAscent215RightWords.right_word_counts

Proof. Machine-checked in Lean as D5/S3/Combinatorics/WeakAscent/WeakAscent215RightWords.right_word_counts (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. David Callan, Toufik Mansour (2025). Ascent Sequences and Weak Ascent Sequences Avoiding a Quadruple of Length-3 Patterns. DOI: 10.5281/zenodo.17144266. URL: https://math.colgate.edu/~integers/z80/z80.pdf.

Commentary.

For every nonnegative length n, the number of weak ascent sequences of length n avoiding 021, 101, 201 and 210, viewed as a rational number, is the coefficient of degree n in the target counting series.

References