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Parents of Vincular-Avoiding Permutations

Abstract

Restricting a 2-41-3-avoiding permutation to its smallest letters preserves avoidance.

Theorem 1.1 (Restriction to an initial set of letters).

Lean statement: D5/S3/Combinatorics/WeakAscent/WeakAscentPermParents.restriction_avoids

Proof. Machine-checked in Lean as D5/S3/Combinatorics/WeakAscent/WeakAscentPermParents.restriction_avoids (✓ 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 permutation of one through n avoiding 2-41-3 and every nonnegative m at most n, retaining only the entries at most m gives a permutation of one through m avoiding 2-41-3.

References