BIT 30 (t990), 583-591 ON GENERATION OF PERMUTATIONS THROUGH DECOMPOSITION OF SYMMETRIC GROUPS INTO COSETS ZBIGNIEW KOKOSIiqSKI Institute of Electrical Engineering and Electronics, Technical University of Krakrw, ut. Warszawska24, 31-155 Krakrw, Poland. Abstract. A hardware-oriented algorithm for generating permutations is presented that takes as a theoretic base an iterative decomposition of the symmetric group Sn into cosets. It generates permutations in a new order. Simple ranking and unranking algorithms are given. The construction of a permutation generator is proposed which contains a cellular permutation network as a main component. The application of the permutation generator for solving a class of combinatorial problems on parallel computers is suggested. C.R. categories: F.1.2, G.2.1. Keywords and Phrases: permutation generation, hardware-oriented algorithm, combinatorial prob- lems, parallel computations. 1. Introduction. Parallel processing of many combinatorial problems solvable by inspection will become possible if the problem of parallel generation of their instances is solved in a proper way. Two different approaches to the parallel generation of combinatorial objects are of interest: 1) design of parallel algorithms for a model of parallel computations with any number of processors, and 2) application of a sequential algorithm (or a parallel algorithm for a given number of processors) to a model of parallel computations in which disjoint subsets of combinatorial objects are distributed among any number of processors (parallel processors). The parallel permutation generation method proposed in this paper may be classified among the second group of solutions. A new sequential algorithm for generation of permutations results from an iterative coset decomposition of the symmetric group S~. A linear order on the set of all n! permutations is defined. Received February 1990. Revised April 1990.