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.
LanguageEnglish
Title of host publicationSurveys in Combinatorics 2013
EditorsSimon R. Blackburn, Stefanie Gerke, Mark Wildon
Pages239-263
Number of pages25
Publication statusPublished - 2013

Publication series

NameLondon Mathematical Society Lecture Note Series
PublisherCambridge University Press
Volume409

Fingerprint

Open Problems
Permutation
M-function
Topological Properties
Poset
Enumeration
Upper bound
Unknown

Keywords

  • permutation patterns
  • permutation patterns theory
  • posets

Cite this

Steingrimsson, E. (2013). Some open problems on permutation patterns. In S. R. Blackburn, S. Gerke, & M. Wildon (Eds.), Surveys in Combinatorics 2013 (pp. 239-263). (London Mathematical Society Lecture Note Series; Vol. 409).
Steingrimsson, Einar. / Some open problems on permutation patterns. Surveys in Combinatorics 2013. editor / Simon R. Blackburn ; Stefanie Gerke ; Mark Wildon. 2013. pp. 239-263 (London Mathematical Society Lecture Note Series).
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Steingrimsson, E 2013, Some open problems on permutation patterns. in SR Blackburn, S Gerke & M Wildon (eds), Surveys in Combinatorics 2013. London Mathematical Society Lecture Note Series, vol. 409, pp. 239-263.

Some open problems on permutation patterns. / Steingrimsson, Einar.

Surveys in Combinatorics 2013. ed. / Simon R. Blackburn; Stefanie Gerke; Mark Wildon. 2013. p. 239-263 (London Mathematical Society Lecture Note Series; Vol. 409).

Research output: Chapter in Book/Report/Conference proceedingChapter

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Steingrimsson E. Some open problems on permutation patterns. In Blackburn SR, Gerke S, Wildon M, editors, Surveys in Combinatorics 2013. 2013. p. 239-263. (London Mathematical Society Lecture Note Series).