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Construction of Combinatorial Objects
, 1995
"... Isomorphism problems often can be solved by determining orbits of a group acting on the set of all objects to be classified. The paper centers around algorithms for this topic and shows how to base them on the same idea, the homomorphism principle. Especially it is shown that forming Sims chains, u ..."
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Isomorphism problems often can be solved by determining orbits of a group acting on the set of all objects to be classified. The paper centers around algorithms for this topic and shows how to base them on the same idea, the homomorphism principle. Especially it is shown that forming Sims chains, using an algorithmic version of Burnside's table of marks, computing double coset representatives, and computing Sylow subgroups of automorphism groups can be explained in this way. The exposition is based on graph theoretic concepts to give an easy explanation of data structures for group actions.
History and Progress of the Generation of Structural Formulae in Chemistry and its Applications
"... After a few remarks on the history of molecular modelling we describe certain mathematical aspects of the generation of molecular structural formulae. The focus is on the automatic generation of structural formulae for the purpose of molecular structure elucidation and the examination of molecular l ..."
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After a few remarks on the history of molecular modelling we describe certain mathematical aspects of the generation of molecular structural formulae. The focus is on the automatic generation of structural formulae for the purpose of molecular structure elucidation and the examination of molecular libraries. The aim is to give a review and to point to relevant literature. We demonstrate an application in the area of quantitative structureproperty/activity relationships. Then, we give a glance on ongoing research in the generation of 3Dstructures (stereoisomers and conformers), and finally we mention two problems that should be solved in the near future, the possible use of hypergraphs, and the generation of patent libraries.
Algebraic Combinatorics in Bayreuth
, 1995
"... I should like to give a brief introduction of our group, describe its main activities in the field of Algebraic Combinatorics, and illustrate them by a few typical examples. 1 ..."
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I should like to give a brief introduction of our group, describe its main activities in the field of Algebraic Combinatorics, and illustrate them by a few typical examples. 1