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Restricted Permutations M D Atkinson

Summary: Restricted Permutations
M D Atkinson
School of Mathematical and Computational Sciences
North Haugh, St Andrews, Fife KY16 9SS, UK
July 20, 2004
Restricted permutations are those constrained by having to avoid sub-
sequences ordered in various prescribed ways. They have functioned as
a convenient descriptor for several sets of permutations which arise natu-
rally in combinatorics and computer science. We study the partial order
on permutations (and more general sequences) that underlies the idea of
restriction and which gives rise to sets of sequences closed under taking
subsequences. In applications, the question of whether a closed set has
a finite basis is often considered. We give a family of sets that have a
finite basis, and then use them to study the inverse problem of describing
a closed set from its basis. We give enumeration results in all cases where
the basis consists of a permutationof length 3 and a permutation of length
4. The paper is an extended version of [2] in that it contains full proofs of
the results presented there which have also been obtained by West [15].
1 General setting


Source: Atkinson, Mike - Department of Computer Science, University of Otago


Collections: Computer Technologies and Information Sciences