 
Summary: Restricted Permutations
M D Atkinson
School of Mathematical and Computational Sciences
North Haugh, St Andrews, Fife KY16 9SS, UK
Abstract
Restricted permutations are those constrained by having to avoid subsequences or
dered in various prescribed ways. They have functioned as a convenient descriptor
for several sets of permutations which arise naturally in combinatorics and com
puter science. We study the partial order on permutations that underlies the idea
of restriction and which gives rise to sets of sequences closed under taking subse
quences. In applications, the question of whether a closed set has a finite basis is
often considered. Several constructions that respect the finite basis property are
given. A family of closed sets, called profileclosed sets, is introduced and used to
solve some instances of the inverse problem: describing a closed set from its basis.
Some enumeration results are also given.
Key words: restricted, forbidden, permutation, sequence, subsequence
1 General setting
The study of permutations which are constrained by not having one or more
subsequences ordered in various prescribed ways has been motivated both by
its combinatorial difficulty and by its appearance in some data structuring
