Pattern Popularity in 132-Avoiding Permutations
Name
Rudolph-2013-Pattern popularity.pdf
Size
288.24 KB
Format
Adobe PDF
Checksum (MD5)
3ebf7b4ac5966609c3c75e467c5835da
Author(s)
Rudolph, Kate
Date Issued
January 2013
Journal
Electronic Journal of Combinatorics
Publisher
Electronic Journal of Combinatorics
Citation
Rudolph, Kate. "Pattern Popularity in 132-Avoiding Permutations." Electronic Journal of Combinatorics, Volume 20, Issue 1 (2013).
Version
Final published version
Abstract
The popularity of a pattern p is the total number of copies of p within all permutations of a set. We address popularity in the set of 132-avoidng permutations. Bona showed that in this set, all other non-monotone length-3 patterns are equipopular, and proved equipopularity relations between some length-k patterns of a specific form. We prove equipopularity relations between general length-k patterns, based on the structure of their corresponding binary plane trees. Our result explains all equipopularity relations for patterns of length up to 7, and we conjecture that it provides a complete classification of equipopularity in 132-avoiding permutations.
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/10.37236/2634
