Let H and K be subgroups of a finite group G . Pick g ? uniformly at random. We study the distribution induced on double cosets. Three examples are treated in detail: 1) = Borel subgroup L n ( F q ) This leads to new theorems for Mallows measure permutations insights into LU matrix factorization. 2) The cosets hyperoctahedral inside S 2 , which applications Ewens's sampling formula mathematical...

Let G be a real form of a complex reductive group. Suppose that we are given involutions σ and θ of G. Let H = G denote the fixed group of σ and let K = G denote the fixed group of θ. We are interested in calculating the double coset space H\G/K. We use moment map and invariant theoretic techniques to calculate the double cosets, especially the ones that are closed. One salient point of our res...

Let G be a real form of a complex reductive group. Suppose that we are given involutions σ and θ of G. Let H = G denote the fixed group of σ and let K = G denote the fixed group of θ. We are interested in calculating the double coset space H\G/K. We use moment map and invariant theoretic techniques to calculate the double cosets, especially the ones that are closed. One salient point of our res...

Billey, Konvalinka, Petersen, Solfstra, and Tenner recently presented a method for counting parabolic double cosets in Coxeter groups, used it to compute $p_n$, the number of $S_n$, $n\leq13$. In this paper, we derive new formula $p_n$ an efficient polynomial time algorithm evaluating formula. We use these results $n\leq5000$ prove asymptotic that was conjectured by Billey et al.

This paper presents a solution of the polycirculant conjecture which states that every vertex-transitive graph G has an automorphism that permutes the vertices in cycles of the same length. This is done by identifying vertex-transitive graphs as coset graphs. For a coset graph H, an equivalence relation ∼ is defined on the vertices of cosets with classes as double cosets of the stabiliser and a...

1. Introduction. It is the purpose of this paper to study some of the properties of the double cosets of a finite group and to prove two main theorems which generalize the results of two previous papers by the author, 2 giving some relations between the double cosets and the irreducible components of the permutation group generated by a given subgroup. We let H be an arbitrary but fixed subgrou...

This paper studies the algebraic structure of transposition hypergroups with idempotent identity. Their subhypergroups and their properties are examined. Right, left and double cosets are defined through symmetric subhypergroups and their properties are studied. Further- more, this paper examines the homomorphisms, the behaviour of attrac- tive and non-attractive elements through them, as well ...

Let G be a connected reductive group over an algebraically closed field k of characteristic not 2; let θ ∈ Aut(G) be an involution and K = Gθ ⊆ G the fixed point group of θ and let P ⊆ G be a parabolic subgroup. The set K\G/P of (K , P)-double cosets in G plays an important role in the study of Harish Chandra modules. In [BH00] we gave a description of the orbits of symmetric subgroups in a fla...

In this paper, we construct eight infinite families of binary linear codes associated with double cosets with respect to certain maximal parabolic subgroup of the special orthogonal group SO−(2n, 2r). Then we obtain four infinite families of recursive formulas for the power moments of Kloosterman sums and four those of 2-dimensional Kloosterman sums in terms of the frequencies of weights in the...