Permutation group algorithms based on partitions, I: Theory and algorithms

Random Remarks on Permutation Group Algorithms

Permutation group algorithms via black box recognition algorithms

If a black box simple group is known to be isomorphic to a classical group over a eld of known characteristic, a Las Vegas algorithm is used to produce an explicit isomorphism. This is used to upgrade all nearly linear time Monte Carlo permutation group algorithms to Las Vegas algorithms when the input group has no composition factor isomorphic to an exceptional group of Lie type or a 3{dimensi...

Permutation Group Algorithms via Black Box

If a black box simple group is known to be isomorphic to a classical group over a field of known characteristic, a Las Vegas algorithm is used to produce an explicit isomorphism. This is used to upgrade all nearly linear time Monte Carlo permutation group algorithms to Las Vegas algorithms when the input group has no composition factor isomorphic to an exceptional group of Lie type or a 3-dimen...

A Method and Two Algorithms on the Theory of Partitions

In this note we describe a general principle for selecting at random from a collection of combinatorial objects, where “at random” means in such a way that each of the objects has equal probability, a priori, of being selected. We apply this principle by displaying two algorithms, the first of which will select a random partition of an integer n, and the second will choose a random partition of...

Quantum Algorithms In Group Theory

We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory.