Abstract. Cyclic sieving is a well-known phenomenon where certain interesting polynomials, especially qanalogues, have useful interpretations related to actions and representations of the cyclic group. We define sieving for an arbitrary group G and study it for the dihedral group I2pnq of order 2n. This requires understanding the generators of the representation ring of the dihedral group. For ...

We consider the dihedral model of motion for chains with fixed edge lengths, in which the angle between every pair of successive edges remains fixed. A chain is flat-state connected if every planar configuration can be transformed to any other via a series of dihedral motions which maintain simplicity. Here we prove that three classes of chains are flat-state connected. The first class is that ...

We give a characterization of limits of dihedral groups in the space of finitely generated marked groups. We also describe the topological closure of dihedral groups in the space of marked groups on a fixed number of generators.

‎Let $Gamma$ be a graph with adjacency eigenvalues $lambda_1leqlambda_2leqldotsleqlambda_n$‎. ‎Then the energy of‎ ‎$Gamma$‎, ‎a concept defined in 1978 by Gutman‎, ‎is defined as $mathcal{E}(G)=sum_{i=1}^n|lambda_i|$‎. ‎Also‎ ‎the Estrada index of $Gamma$‎, ‎which is defined in 2000 by Ernesto Estrada‎, ‎is defined as $EE(Gamma)=sum_{i=1}^ne^{lambda_i}$‎. ‎In this paper‎, ‎we compute the eigen...

In this paper, we find a strong new restriction on the structure of CI-groups. We show that, if R is generalised dihedral group and CI-group, then for every odd prime p Sylow p-subgroup has order p, or 9. Consequently, any CI-group with quotient same restriction, that

metal—polyaniline nanocomposites such as platinum-polyaniline nanocomposite is prepared by insitu oxidative polymerization of aniline and reduction of pt+4 ions into pt nanoparticles. thepolymerization of aniline was carried out in the presence of 1(2ptcn6 [potassium hexa cyanoplatinate (iv)] as oxidizing agent. during the reaction aniline monomers undergo oxidation andform polyaniline (pant) w...