Generating Trees and Pattern Avoidance in Alternating Permutations

  • Joel Brewster Lewis

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 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.

Published
2012-01-16
Article Number
P21