2013/10/22 by Jonathan Bloom, Bloom, Jonathan, Vince Vatter +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #math.CO #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1310.6073
openalex publication_date 2013/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.