A survey of simple permutations

Brignall, Robert (2010). A survey of simple permutations. In: Linton, Steve; Ruškuc, Nik and Vatter, Vincent eds. Permutation Patterns. London Mathematical Society Lecture Notes Series (376). Cambridge, UK: Cambridge University Press, pp. 41–65.

URL: http://www.cambridge.org/catalogue/catalogue.asp?i...

Abstract

We survey the known results about simple permutations. In particular, we present a number of recent enumerative and structural results pertaining to simple permutations, and show how simple permutations play an important role in the study of permutation classes. We demonstrate how classes containing only finitely many simple permutations satisfy a number of special properties relating to enumeration, partial well-order and the property of being finitely based.

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