Equipopularity Classes of 132-Avoiding Permutations
Name
Chua-2014-Equipopularity classes.pdf
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295.22 KB
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Checksum (MD5)
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Author(s)
Chua, Lynn
Sankar, Krishanu Roy
Date Issued
March 2014
Journal
Electronic Journal of Combinatorics
Publisher
Electronic Journal of Combinatorics
Citation
Chua, Lynn, and Krishanu Roy Sankar. "Equipopularity Classes of 132-Avoiding Permutations." Electronic Journal of Combinatorics, Volume 21, Issue 1 (2014).
Version
Final published version
Abstract
The popularity of a pattern p in a set of permutations is the sum of the number of copies of p in each permutation of the set. We study pattern popularity in the set of 132-avoiding permutations. Two patterns are equipopular if, for all n, they have the same popularity in the set of length-n 132-avoiding permutations. There is a well-known bijection between 132-avoiding permutations and binary plane trees. The spines of a binary plane tree are defined as the connected components when all edges connecting left children to their parents are deleted, and the spine structure is the sorted sequence of lengths of the spines. Rudolph shows that patterns of the same length are equipopular if their associated binary plane trees have the same spine structure. We prove the converse of this result using the method of generating functions, which gives a complete classification of 132-avoiding permutations into equipopularity classes.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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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/10.37236/3675
