 
Summary: Permuting mechanisms and closed classes of
permutations
M.D. Atkinson
Robert Beals
December 16, 1998
1 Introduction
A permuting mechanism M is a device that accepts any finite input sequence
of objects (normally denoted by 1, 2, . . . ) and produces a permutation of these
objects. We let perm(M) denote the set of possible permutations that M might
produce.
Examples
1. A ri#e shu#er divides the input sequence into two segments 1, 2, . . . , m
and m+1, . . . , n and then interleaves them in any way. Thus perm(M) =
{1, 12, 21, 123, 132, 213, 231, 312, 1234, 1243, 1342, . . . etc.}
2. A stack receives members of the input sequence and outputs them under
a lastinfirstout discipline
3. A transportation network [2] is any finite directed graph with a node to
represent the input queue and a node to represent the output queue. The
other nodes can each hold one of the input objects and the objects are
moved around the graph until they emerge at the output node
