Regular closed sets of permutations

Authors:
M. H. Albert;M. D. Atkinson;N. Ruškuc
Affiliations:
Department of Computer Science, University of Otago, New Zealand;Department of Computer Science, University of Otago, New Zealand;School of Mathematics and Statistics, University of St Andrews, UK
Venue:
Theoretical Computer Science
Year:
2003

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Abstract

Machines whose main purpose is to permute and sort data are studied. The sets of permtutations that can arise are analysed by means of finite automata and avoided pattern techniques. Conditions are given for these sets to be enumerated by rational generating functions. As a consequence we give the first non-trivial examples of pattern closed sets of permutations all of whose closed subclasses have rational generating functions.