We prove that the pseudorandom generator introduced in [INW94] fools group products of a given finite group. The seed length is O(log n log 1 ), where n the length of the word and...
We present various techniques to count proportions of permutations with restricted cycle structure in finite permutation groups. For example, we show how a generalized block theo...
Factorizations of the cyclic permutation (1 2 . . . N) into two permutations with respectively n and m cycles, or, equivalently, unicellular bicolored maps with N edges and n whit...
We study the random composition of a small family of O(n3 ) simple permutations on {0, 1}n . Specifically we ask how many randomly selected simple permutations need be composed to...
An uncovering-by-bases for a group G acting on a finite set is a set U of bases for G such that any r-subset of is disjoint from at least one base in U, where r is a parameter d...