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 A[subscript 2n](2143) of alternating permutations of length 2n avoiding 2143 and the set of stan...

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Bibliographic Details
Main Author: Lewis, Joel Brewster (Contributor)
Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
Format: Article
Language:English
Published: Electronic Journal of Combinatorics, 2014-09-18T15:57:37Z.
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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[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.