We use an interesting result of probabilistic flavor concerning the product of two permutations consisting of one cycle each to find an explicit formula for the average number of block interchanges needed to sort a permutation of length n.

We study a family of permutations of the finite field Fqn given by x + γ f(x), where γ ∈ Fqn and f : Fqn → Fq. In particular, we determine the cycle structure and the inverse of such a permutation.

by a quasi-permutation matrix we mean a square matrix over the complex field c with non-negative integral trace. thus every permutation matrix over c is a quasipermutation matrix. for a given finite group g, let p(g) denote the minimal degree of a faithful permutation representation of g (or of a faithful representation of g by permutation matrices), let q(g) denote the minimal degree of a fait...

Abstract In our previous work, we equipped quiver Grassmannians for nilpotent representations of the equioriented cycle with an action algebraic torus. We show here that equivariant cohomology ring is acted upon by a product symmetric groups and investigate this permutation via GKM techniques. case (type A) flag varieties, or Schubert varieties therein, recover Tymoczko’s results on representat...

We present various results on multiplying cycles in the symmetric group. One result is a generalisation of the following theorem of Boccara (1980): the number of ways of writing an odd permutation in the symmetric group on n symbols as a product of an n-cycle and an (n − 1)-cycle is independent of the permutation chosen. We give a number of different approaches of our generalisation. One partia...

This paper studies the cycle indices of products of permutation groups. The main focus is on the product action of the direct product of permutation groups. The number of orbits of the product on n-tuples is trivial to compute from the numbers of orbits of the factors; on the other hand, computing the cycle index of the product is more intricate. Reconciling the two computations leads to some i...