Generating Trees and Pattern Avoidance in Alternating Permutations

Abstract

We extend earlier work of the same author to enumerate alternating permutations avoiding the permutation pattern 2143. We use a generating tree approach to construct a recursive bijection between the set A[subscript 2n](2143) of alternating permutations of length 2n avoiding 2143 and the set of standard Young tableaux of shape ⟨n,n,n⟩, and between the set A[subscript 2n+1](2143) of alternating permutations of length 2n+1 avoiding 2143 and the set of shifted standard Young tableaux of shape ⟨n+2,n+1,n⟩. We also give a number of conjectures and open questions on pattern avoidance in alternating permutations and generalizations thereof.