Alternating, Pattern-Avoiding Permutations
Name
Lewis-2009-Alternating pattern-avoiding.pdf
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97.88 KB
Format
Adobe PDF
Checksum (MD5)
2332e6c8db01bafe545e24840aabe87d
Author(s)
Lewis, Joel Brewster
Date Issued
February 2009
Journal
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
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.37236/245
