We survey algorithms to compute with large finite permutation and matrix groups. Particular attention will be given to handling both types of groups with similar methods, using structural properties to answer even basic questions such as the order of the input group. Mathematics Subject Classification (2000). Primary 20B40; Secondary 20B15.

We describe the use of sorting networks to form relaxations of problems involving permutations of n objects. This approach is an alternative to relaxations based on the Birkhoff polytope (the set of n × n doubly stochastic matrices), providing a more compact formulation in which the only constraints are box constraints. Using this approach, we form a variant of the relaxation of the quadratic a...

The most general flowshop scheduling problem is also addressed in the literature as nonpermutation flowshop (NPFS). Current processors are able to cope with the (n!) m combinatorial complexity of non-permutation flowshop scheduling by metaheuristics. After briefly discussing the requirements for a manufacturing layout to be designed and modeled as non-permutation flowshop, a disjunctive graph (...

The paper introduces an approach for crosstalk-free bitpermute-complement (BPC) permutations routing in hybrid optical variable-stage shuffle-exchange networks (SENs) of size where N=2, and the number of stages can vary in . The number of stages should be asserted as required by a given BPC permutation for its admissibility. The crosstalk is caused by interacting of two optical signals within t...

Sorting by Transpositions is an NP-hard problem for which several polynomial-time approximation algorithms have been developed. Hartman and Shamir (2006) developed a 1.5-approximation [Formula: see text] algorithm, whose running time was improved to O(nlogn) by Feng and Zhu (2007) with a data structure they defined, the permutation tree. Elias and Hartman (2006) developed a 1.375-approximation ...

Known doubly transitive permutation groups are well studied and the classification of all doubly transitive groups has been done by applying the classification of the finite simple groups. Readers may refer to [6]. This may mean that it is not still sufficient to study doubly transitive groups as permutation groups. Typical arguments on doubly transitive groups are seen in the book[3]. In the p...

In order to sequence the tasks of a job shop problem (JSP) on a number of machines related to the technological machine order of jobs, a new representation technique { mathematically known as \permutation with repetition" is presented. The main advantage of this single chromosome representation is { in analogy to the permutation scheme of the traveling salesman problem (TSP) { that it cannot pr...

Let p be a prime and q a power of p. We study the permutation properties of the polynomial gn,q ∈ Fp[x] defined by the functional equation ∑ a∈Fq (x + a) n = gn,q(x − x). The polynomial gn,q is a q-ary version of the reversed Dickson polynomial in characteristic 2. We are interested in the parameters (n, e; q) for which gn,q is a permutation polynomial (PP) of Fqe . We find several families of ...

To date, testing interactions in high dimensions has been a challenging task. Existing methods often have issues with sensitivity to modeling assumptions and heavily asymptotic nominal p-values. To help alleviate these issues, we propose a permutation-based method for testing marginal interactions with a binary response. Our method searches for pairwise correlations which differ between classes...

Abstract The form of the leptonic mixing matrix emerging from experiment has, in the last few years, generated a lot of interest in the so-called tribimaximal type. This form may be naturally associated with the possibility of a discrete permutation symmetry (S3) among the three generations. However, trying to implement this attractive symmetry has resulted in some problems and it seems to have...