We give an O(n lg n)-time algorithm for counting the number of inversions in a permutation on n elements. This improves a long-standing previous bound of O(n lg n/ lg lg n) that ...
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...
We define an excedance number for the multi-colored permutation group i.e. the wreath product (Zr1 × · · · × Zrk ) Sn and calculate its multi-distribution with some natural ...
Through the use of a new disk-based method for enumerating very large orbits, condensation for orbits with tens of billions of elements can be performed. The algorithm is novel in...