# A compact representation for permutation groups

@article{Jerrum1982ACR, title={A compact representation for permutation groups}, author={Mark Jerrum}, journal={23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)}, year={1982}, pages={126-133} }

An O(n2) space representation for permutation groups of degree n is presented. The representation can be constructed in time O(n5), and supports fast membership testing. Applications of the representation to the generation of systems of coset representatives, and of complete block systems, are discussed.

## 79 Citations

On the diameter of permutation groups

- MathematicsSTOC
- 1983

We show that any group represented by generators that are cycles of bounded degree has O(n2) diameter, i.e., that the longest product of generators required to reach any permutation in the group is…

The parallel complexity of the abelian permutation group membership problem

- Mathematics24th Annual Symposium on Foundations of Computer Science (sfcs 1983)
- 1983

We show that the permutation group membership problem can be solved in depth (logn)3 on a Monte Carlo Boolean circuit of polynomial size in the restricted case in which the group is abelian. We also…

On the length of subgroup chains in the symmetric group

- Mathematics, Computer Science
- 1986

It is proved that for n≥2, the length of every subgroup chain in Sn is at most 2n-3, which has applications to worst case complexity estimates for permutation group algorithms.

Fast management of permutation groups

- Computer Science[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science
- 1988

Novel algorithms for computation in permutation groups are presented. They provide an order-of-magnitude improvement in the worst-case analysis of the basic permutation-group problems, including…

Fast Management of Permutation Groups I

- Computer ScienceSIAM J. Comput.
- 1997

New algorithms for permutation group manipulation result in an improvement of nearly an order of magnitude in the worst-case analysis for the fundamental problems of finding strong generating sets and testing membership.

Construction of Combinatorial Objects

- Computer Science
- 1997

The paper centers around algorithms for this topic and shows how to base them on the same idea, the homomorphism principle, and shows that forming Sims chains, using an algorithmic version of Burnside's table of marks, computing double coset representatives, and computing Sylow subgroups of automorphism groups can be explained in this way.

Fast Group Membership Using a Strong Generating Test for Permutation Groups

- Computer Science, MathematicsComputers and Mathematics
- 1989

An algorithm is presented here which has an observed running time of O(n 4) for all permutations groups for which it has been tested and which has a new test for whether a set of generators is a strong generating set.

Minimum Bases for Permutation Groups: The Greedy Approximation

- Computer Science, MathematicsJ. Algorithms
- 1992

Zero-Knowledge Proofs of the Conjugacy for Permutation Groups

- Mathematics, Computer ScienceArXiv
- 2008

A perfect zero-knowledge proof system for recognition if two permutation groups are conjugate is designed.

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