Summary: Simple permutations and pattern restricted
Department of Computer Science
University of Otago, Dunedin, New Zealand.
A simple permutation is one that does not map any non-trivial
interval onto an interval. It is shown that, if the number of simple
permutations in a pattern restricted class of permutations is finite,
the class has an algebraic generating function and is defined by a fi-
nite set of restrictions. Some partial results on classes with an infinite
number of simple permutations are given. Examples of results obtain-
able by the same techniques are given; in particular it is shown that
every pattern restricted class properly contained in the 132-avoiding
permutations has a rational generating function.
1 Introduction and definitions
In  Simion and Schmidt managed to enumerate the number of permu-
tations of each length that avoided some arbitrary given set of permutation