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...

In other words, a coset is what we get when we take a subgroup and shift it (either on the left or on the right). The best way to think about cosets is that they are shifted subgroups, or translated subgroups. Note g lies in both gH and Hg, since g = ge = eg. Typically gH 6= Hg. When G is abelian, though, left and right cosets of a subgroup by a common element are the same thing. When an abelia...

I review some marginal deformations of SU(2) and SL(2, R) Wess–Zumino–Witten models , which are relevant for the investigation of the moduli space of NS5/F1 brane configurations. Particular emphasis is given to the asymmetric deformations, triggered by electric or magnetic fluxes. These exhibit critical values, where the target spaces become exact geometric cosets such as S 2 ≡ SU(2)/U(1) or Ad...

The duality symmetry group of the cosets SU(n, 1) SU(n)⊗ U(1) , which describe the moduli space of a two-dimensional subspace of an orbifold model with (n − 1) complex Wilson lines moduli, is discussed. The full duality group and its explicit action on the moduli fields are derived. ∗ e-mail: [email protected]. 1 The derivation of a field theoretic low-energy effective action from string ...

Several interesting features of coset models " without fixed points " are easily understood via Chern-Simons theory. In this paper we derive explicit formulae for the handle-squashing operator in these cosets. These operators are fixed, linear combinations of the irreducible representations of the coset. As a simple application of these curious formulae, we compute the traces of all genus-one o...

Recently Golay complementary sets were shown to exist in the subsets of second-order cosets of a q-ary generalization of the first-order Reed–Muller (RM) code. We show that mutually orthogonal Golay complementary sets can also be directly constructed from second-order cosets of a q-ary generalization of the first-order RM code. This identification can be used to construct zero correlation zone ...

This paper is devoted to finding solutions of polynomial equations in roots of unity. It was conjectured by S. Lang and proved by M. Laurent that all such solutions can be described in terms of a finite number of parametric families called maximal torsion cosets. We obtain new explicit upper bounds for the number of maximal torsion cosets on an algebraic subvariety of the complex algebraic n-to...

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...

Let B be the binary two-error-correcting BCH code of length 2" 1 and let B be the extended code of B. We give formal expressions of weight distributions of the cosets of the codes B only depending on m. We can then deduce the weight distributions of the cosets of B. When m is odd, it is well known that there are four distinct weight distributions for the cosets of B . So our main result is abou...