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Restricted permutations and the wreath M.D. Atkinson

Summary: Restricted permutations and the wreath
M.D. Atkinson
Department of Computer Science,University of Otago, P.O. Box 56,Dunedin, New
T. Stitt
School of Computer Science,North Haugh, St Andrews, Fife KY16 9SS, UK
Restricted permutations are those constrained by having to avoid subsequences
ordered in various prescribed ways. A closed set is a set of permutations all satisfying
a given basis set of restrictions. A wreath product construction is introduced and
it is shown that this construction gives rise to a number of useful techniques for
deciding the nite basis question and solving the enumeration problem. Several
applications of these techniques are given.
Key words: restricted, forbidden, permutation, sequence, subsequence, basis,
1 Introduction
This article is a sequel to [1]. In that paper we studied the partial order
\involvement" on permutations and argued that it should be studied through
ideals called closed sets. Closed sets are a natural setting for many combinato-


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


Collections: Computer Technologies and Information Sciences