@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",
}