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Discrete Mathematics for Combinatorial Chemistry
, 1998
"... The aim is a description of discrete mathematics used in a project devoted to the implementation of a software package for the simulation of combinatorial chemistry. ..."
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The aim is a description of discrete mathematics used in a project devoted to the implementation of a software package for the simulation of combinatorial chemistry.
Algorithms for Group Actions: Homomorphism Principle and Orderly Generation Applied to Graphs
 OF DIMACS SERIES IN DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
, 1996
"... The generation of discrete structures up to isomorphism is interesting as well for theoretical as for practical purposes. Mathematicians want to look at and analyse structures and for example chemical industry uses mathematical generators of isomers for structure elucidation. The example chosen in t ..."
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The generation of discrete structures up to isomorphism is interesting as well for theoretical as for practical purposes. Mathematicians want to look at and analyse structures and for example chemical industry uses mathematical generators of isomers for structure elucidation. The example chosen in this paper for explaining general generation methods is a relatively far reaching and fast graph generator which should serve as a basis for the next more powerful version of MOLGEN, our generator of chemical isomers.
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.
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
Mathematical Simulations in Combinatorial Chemistry
, 1996
"... A novel technique for chemical synthesis in drug research is combinatorial chemistry, where usually a set of buildingblock molecules is attached to a core structure in all the combinatorially possible ways. The resulting set of compounds (called a library) can then be systematically screened for a ..."
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A novel technique for chemical synthesis in drug research is combinatorial chemistry, where usually a set of buildingblock molecules is attached to a core structure in all the combinatorially possible ways. The resulting set of compounds (called a library) can then be systematically screened for a desired biological activity. In this paper we discuss ways and limits of a mathematical simulation of this procedure. At first, two methods for selecting the buildingblocks from a given structure pool are presented with the objective to obtain only dissilimar library entries. Next an algorithm is described for the exhaustive and redundancyfree generation of a combinatorial library, illustrated by a singlestep and a multicomponent reaction. Finally equations for the enumeration of the library sizes are derived and the limits of the virtual combinatorial chemistry, i.e. purely in computer and without experiment, are discussed. 1