Restricted permutations and the wreath product

Authors:
M. D. Atkinson;T. Stitt
Affiliations:
Department of Computer Science, University of Otago, P.O. Box 56, Dunedin, New Zealand;School of Computer Science, North Haugh, St Andrews, Fife KY16 9SS, UK
Venue:
Discrete Mathematics
Year:
2002

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Abstract

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 finite basis question and solving the enumeration problem. Several applications of these techniques are given.