 
Summary: Compositions of pattern restricted sets of
permutations
M. H. Albert
R. E. L. Aldred
M. D. Atkinson
H. P. van Ditmarsch
C. C. Handley
D. A. Holton
D. J. McCaughan
September 3, 2004
Abstract
The composition of two pattern restricted classes X, Y is the set of all
permutation products where X, Y . This set is also defined
by pattern restrictions. Examples are given where this set of restrictions
is finite and where it is infinite. The composition operation is studied
in terms of machines that sort and generate permutations. The theory
is then applied to a multistage sorting network where each stage can
exchange any number of adjacent disjoint pairs.
1 Introduction
In the theory of pattern restricted permutations it is normal to regard per
