Generating trees and pattern avoidance in alternating permutations (Q426780)

Summary: 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 \(A_{2n}(2143)\) of alternating permutations of length \(2n\) avoiding \(2143\) and the set of standard Young tableaux of shape \(\langle n, n, n\rangle\), and between the set \(A_{2n + 1}(2143)\) of alternating permutations of length \(2n + 1\) avoiding \(2143\) and the set of shifted standard Young tableaux of shape \(\langle n + 2, n + 1, n\rangle\). We also give a number of conjectures and open questions on pattern avoidance in alternating permutations and generalizations thereof.