On Parallel Generation of Partial Derangements, Derangements and Permutations

The concept of a partial derangement is introduced and a versatile representation of partial derangements is proposed with permutations and derangements as special cases. The representation is derived from a representation of permutations by iterative decomposition of symmetric permutation group Sn into cosets. New algorithms are proposed for generation of partial set derangements in t. The control sequences produced by the generation algorithms appear either in lexicographic or reverse lexicographic order while the output sequences representing partial derangements are obtained from the control sequences in corresponding linear orders. A parallel hardware implementation of the generator of partial derangements is described.