@inbook{d262ea75670a4216930802e2a98219c7,

title = "Some open problems on permutation patterns",

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.",

keywords = "permutation patterns, permutation patterns theory, posets",

author = "Einar Steingrimsson",

year = "2013",

language = "English",

isbn = "9781107651951",

series = "London Mathematical Society Lecture Note Series",

publisher = "Cambridge University Press",

pages = "239--263",

editor = "Blackburn, {Simon R.} and Stefanie Gerke and Mark Wildon",

booktitle = "Surveys in Combinatorics 2013",

address = "United Kingdom",

}