Pattern popularity in 132-avoiding permutations
type: Item
instance of: scholarly article
title: Pattern popularity in 132-avoiding permutations
zbMATH Open document ID: 1267.05013
author: Kate Rudolph
published in: The Electronic Journal of Combinatorics
publication date: 2013-06-07T00:00:00Z
full work available at URL: v20i1p8
review text: Summary: 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. \textit{M. Bóna} [ibid. 19, No. 1, Research Paper P62, 11 p., electronic only (2012; Zbl 1243.05006)] 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.
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05A19
zbMATH DE Number: 6171847
zbMATH Keywords: permutations
zbMATH Keywords: pattern-avoidance
zbMATH Keywords: pattern popularity
zbMATH Keywords: equipopular patterns
zbMATH Keywords: equipopularity relations
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6171847