The generation of molecular graphs by computer programs has undergone some changes. The development is reported with focus on various mathematical methods that are created and employed in this process. No attempt has been made to explicitely state and prove the theorems but this overview contains hints to the relevant literature. In particular, a new generator MOLGEN 4.0 is described that aims ...

Fundamental tools of molecular structure elucidation are computer programs generating constitutional isomers and configurational isomers. A general disadvantage of the methods of algebraic stereoisomer generation by Nourse, Smith, Carhart and Djerassi is the restriction of the valences of the stereocenters to four. The present paper discusses an extension of this concept to higher-valence cente...

Solution: For the action mentioned in the hint, the stabilizer of the coset eH (e is the identity) is H since gH = H implies that g ∈ H. The kernel K of the homomorphism of G into the permutation group of the cosets is a normal subgroup of G which is the intersection of stabilizers of all cosets. In particular the kernel K of the above homomorphism is a subgroup of H. Its index in G is equal to...

How far can the elementary description of centralizers of parabolic subalgebras of Hecke algebras of finite real reflection groups be generalized to the complex reflection group case? In this paper we begin to answer this question by establishing results in two directions. First, under conditions closely analogous to those existing for the real case, we give explicit relations between coefficie...

Abstract We use [11] to study the algebra structure of twisted cotriangular Hopf algebras ${}_J\mathcal{O}(G)_{J}$, where $J$ is a $2$-cocycle for connected nilpotent algebraic group $G$ over $\mathbb{C}$. In particular, we show that ${}_J\mathcal{O}(G)_{J}$ an affine Noetherian domain with Gelfand–Kirillov dimension $\dim (G)$, and if unipotent supported on $G$, then ${}_J\mathcal{O}(G)_{J}\co...

Entanglement distillation is an essential building block in quantum communication protocols. Here, we study the class of near-term implementable protocols that use bilocal Clifford operations followed by a single round communication. We introduce tools to enumerate and optimise over all for up $n=5$ (not necessarily equal) Bell-diagonal states using commodity desktop computer. Furthermore, expl...

Symmetry simplifications are introduced in configuration interaction (CI) by reducing the number of symmetry-allowed space types if there is degeneracy in some of the molecular orbitals by constructing the unique space types. A new symmetry group which we call the configuration symmetry group is defined and is shown to be expressible as a generalized wreath product group. Generating functions a...

The transfer homomorphism from a group G to an abelian subgroup H of finite index in G arises from the natural action of G on the cosets of H. It plays an important role in the study of unsolvable groups and aids in the characterization of groups in which all Sylow p-subgroups are cyclic. In this paper, we will define the transfer homomorphism, and then investigate a few of its properties. Let ...

Symmetry simplifications are introduced in configuration interaction (CI) by reducing the number of symmetry-allowed space types if there is degeneracy in some of the molecular orbitals by constructing the unique space types. A new symmetry group which we call the configuration symmetry group is defined and is shown to be expressible as a generalized wreath product group. Generating functions a...