Two Vignettes On Full Rook Placements

Abstract

Using bijections between pattern-avoiding permutations and certain full rook placements on Ferrers boards, we give short proofs of two enumerative results. The first is a simplified enumeration of the 3124, 1234-avoiding permutations, obtained recently by Callan via a complicated decomposition. The second is a streamlined bijection between 1342-avoiding permutations and permutations which can be sorted by two increasing stacks in series, originally due to Atkinson, Murphy, and Ruškuc.

9 pages, 4 figures

References in corpus (2)

• Permutations avoiding 4321 and 3241 have an algebraic generating function
• Pattern avoidance in matchings and partitions

Cited by in corpus (2)

• Patterns in Permutations and Involutions: A Structural and Enumerative Approach
• Passing through a stack $k$ times with reversals