Generating Trees and Pattern Avoidance in Alternating Permutations

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 A2n(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 A2n+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.