Alternating, Pattern-Avoiding Permutations
Author(s)
Lewis, Joel Brewster
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We study the problem of counting alternating permutations avoiding collections of permutation patterns including 132. We construct a bijection between the set S[subscript n](132) of 132-avoiding permutations and the set A[subscript 2n+1](132) of alternating, 132-avoiding permutations. For every set p[subscript 1],…,p[subscript k] of patterns and certain related patterns q[subscript 1],…,q[subscript k], our bijection restricts to a bijection between S[subscript n](132,p[subscript 1],…,p[subscript k]), the set of permutations avoiding 132 and the p[subscript i], and A[subscript 2n+1](132,q[subscript 1],…,q[subscript k]), the set of alternating permutations avoiding 132 and the q[subscript i]. This reduces the enumeration of the latter set to that of the former.
Date issued
2009-02Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Electronic Journal of Combinatorics
Publisher
Electronic Journal of Combinatorics
Citation
Lewis, Joel Brewster. "Alternating, Pattern-Avoiding Permutations." Electronic Journal of Combinatorics, Volume 16, Issue 1 (2009).
Version: Final published version
ISSN
1077-8926