A (multi)hypergraph H with vertices in N contains a permutation p = a1a2 . . . ak of 1, 2, . . . , k if one can reduce H by omitting vertices from the edges so that the resulting ...
We show that any quantum algorithm to decide whether a function f : [n] → [n] is a permutation or far from a permutation must make Ω n1/3 /w queries to f, even if the algorith...
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 ...
This paper addresses an aspect of controllability in a single-leader network when the agents are homogeneous. In such a network, indices are not assigned to the individual agents a...
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...