Reinhard Laue

MOLGEN+, a generator of connectivity isomers and stereoisomers for molecular structure elucidation

The structure generator MOLGEN produces all the molecular graphs that correspond to a given chemical formula and (optionally) prescribed and forbidden substructures as well as further optional conditions like intervals for possible ring sizes, hybridization of carbon atoms (not completely implemented), etc. It does this in a fast and redundancy free way, which seems, to our knowledge, to be more efficient than all the other molecular generators known [see R. Grund, A. Kerber and R. Laue, MATCH, 27 (1992) 87, for introductions to various other generators]. Afterwards these molecular graphs can be displayed on the computer screen, 3D-placements of them (using an energy model) can be computed, and the stereoisomers can be calculated and visualized basing on this placement. Therefore, this generator serves very well as the mathematical core of computer packages for molecular structure elucidation. Moreover, it can easily be used for demonstrations in chemical education. MOLGEN developed from MOLGRAPH [introduced in A. Kerber, R. Laue and D. Moser, Anal. Chim. Acta, 235 (1990) 221]. In contrast to MOLGRAPH it has a much wider range of application since it does not need a catalog of precomputed cyclic substructures.

MOLGEN-CID: A canonizer for molecules and graphs accessible through the internet

The MOLGEN Chemical Identifier MOLGEN-CID is a software module freely accessible via the Internet. For a molecule or graph entered in molfile format (2D) it produces, by a canonical renumbering procedure, a canonical molfile and a unique character string that is easily compared by computer to a similar string. The mode of operation of MOLGEN-CID is detailed and visualized with examples.

Simple 8-Designs with Small Parameters

We show the existence of simple 8-(31,10,93) and 8-(31,10,100) designs. For each value of λ we show 3 designs in full detail. The designs are constructed with a prescribed group of automorphisms PSL(3,5) using the method of Kramer and Mesner KramerMesner76. They are the first 8-designs with small parameters which are known explicitly. We do not yet know if PSL(3,5) is the full group of automorphisms of the given designs. There are altogether 138 designs with λ = 93 and 1658 designs with λ = 100 and PSL(3,5) as a group of automorphisms. We prove that they are all pairwise non-isomorphic. For this purpose, a brief account on the intersection numbers of these designs is given. The proof is done in two different ways. At first, a quite general group theoretic observation shows that there are no isomorphisms. In a second approach we use the block intersection types as invariants, they classify the designs completely.

The Discovery of Simple 7-Designs with Automorphism Group PTL (2, 32)

A computer package is being developed at Bayreuth for the generation and investigation of discrete structures. The package is a C and C++ class library of powerful algorithms endowed with graphical interface modules. Standard applications can be run automatically whereas research projects mostly require small C or C++ programs. The basic philosophy behind the system is to transform problems into standard problems of e.g. group theory, graph theory, linear algebra, graphics, or databases and then to use highly specialized routines from that field to tackle the problems. The transformations required often follow the same principles especially in the case of generation and isomorphism testing.

New large sets of t-designs

Abstact: We introduce generalizations of earlier direct methods for constructing large sets of t-designs. These are based on assembling systematically orbits of t-homogeneous permutation groups in their induced actions on k-subsets. By means of these techniques and the known recursive methods we construct an extensive number of new large sets, including new infinite families. In particular, a new series of LS[3](2(2 + m), 8·3m − 2, 16·3m − 3) is obtained. This also provides the smallest known ν for a t-(ν, k, λ) design when t ≥ 16. We present our results compactly for ν ≤ 61, in tables derived from Pascals triangle modulo appropriate primes.

Ein strukturgenerator für molekulare graphen

Abstract ( A structure generator for molecular graphics. ) The structure generator presented is suitable for molecular structure elucidation. The generator is self-standing and can (in suitable cases) construct a nonredundant exhaustive list of connected multigraphs with appropriate ranking and prescribed or forbidden subgraphs.

Group Actions, Double Cosets, and Homomorphisms: Unifying Concepts for the Constructive Theory of Discrete Structures

In the present paper we describe the use of group actions, double cosets and homomorphisms in the constructive theory of discrete structures, as we found it useful from both a theoretical and a practical point of view. By means of examples we should like to demonstrate that these methods are useful both as unifying principles and as efficient methods for applications.

Large sets of subspace designs

In this article, three types of joins are introduced for subspaces of a vector space. Decompositions of the Gra{\ss}mannian into joins are discussed. This framework admits a generalization of large set recursion methods for block designs to subspace designs. We construct a

MOLGEN 5.0, a Molecular Structure Generator

2

A Steiner 5-Design on 36 Points

-