Some open problems on permutation patterns

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

This is a brief survey of some open problems on permutation patterns, with an emphasis on subjects not covered in the recent book by Kitaev, \emph{Patterns in Permutations and words}. I first survey recent developments on the enumeration and asymptotics of the pattern 1324, the last pattern of length 4 whose asymptotic growth is unknown, and related issues such as upper bounds for the number of avoiders of any pattern of length k for any given k. Other subjects treated are the M\"obius function, topological properties and other algebraic aspects of the poset of permutations, ordered by containment, and also the study of growth rates of permutation classes.
Original languageEnglish
Title of host publicationSurveys in Combinatorics 2013
EditorsSimon R. Blackburn, Stefanie Gerke, Mark Wildon
PublisherCambridge University Press
Pages239-263
Number of pages25
ISBN (Print)9781107651951
Publication statusPublished - 2013

Publication series

NameLondon Mathematical Society Lecture Note Series
PublisherCambridge University Press
Volume409

Keywords

  • permutation patterns
  • permutation patterns theory
  • posets

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