Permuting mechanisms and closed classes of permutations 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 Collections: Computer Technologies and Information Sciences