It is well-known that concentrators are sparse graphs of high connectivity, which play a key role in the construction of switching networks; and any semi-vertex transitive graph is isomorphic to a bi-coset graph. In this paper, we prove that random bi-coset graphs are almost always concentrators, and construct some examples of semi-vertex transitive concentrators.

We perform the bosonic dualisation of the matter coupled N = 1, D = 9 supergravity. We derive the Lie superalgebra which parameterizes the coset map whose Cartan form realizes the second-order bosonic field equations. Following the non-linear coset construction we present the first-order formulation of the bosonic field equations as a twisted self-duality condition.

Inspired by Lie algebra expansion, we consider an extension of the introduced in A. Fontanella and S. J. van Tongeren [Coset space actions for nonrelativistic strings, High Energy Phys. 06 (2022) 80.] string coset action ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{5}$. We show that extended admits a nondegenerate inner product which is adjoint invariant under full algebra...

Let K be a finite field of characteristic p . We study certain class functions → that agree with an F -affine function on each coset given additive subgroup W – we call them W-coset-wise show these form permutation group the structure imprimitive wreath product and characterize which are complete mappings As consequence, able to provide various new examples cycle types for instance, if > 2 , th...

We consider a uni ed setting for studying local valuated groups and coset-valuated groups, emphasizing the associated ltrations rather than the values of elements. Stable exact sequences, projectives and injectives are identi ed in the encompassing category, and in the category corresponding to coset-valuated groups.

The dualisation and the first-order formulation of the D = 7 abelian Yang-Mills supergravity which is the low energy effective limit of the D = 7 fully Higssed heterotic string is discussed. The nonlinear coset formulation of the scalars is enlarged to include the entire bosonic sector by introducing dual fields and by constructing the Lie superalgebra which generates the dualized coset element.

We present formulae for the characters of coset conformal field theories and apply these to specific examples to determine the integer shift of the conformal weights of primary fields. We also present an example of a coset conformal field theory which cannot be described by the identification current method.

In this paper, we introduce a class of double coset cayley digraphs induced by right solvable ward groupoids. These class of graphs can be viewed as a generalization of double coset cayley graphs induced by groups. Further, many graph properties are expressed in terms of algebraic properties.