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Isomorphfree exhaustive generation of combinatorial designs
, 2002
"... This report investigates algorithmic isomorphfree exhaustive generation of balanced incomplete block designs (BIBDs), resolvable balanced incomplete block designs (RBIBDs), and the corresponding resolutions. In particular, three algorithms for isomorphfree exhaustive generation of (v, k, λ)BIBDs ..."
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Cited by 3 (0 self)
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This report investigates algorithmic isomorphfree exhaustive generation of balanced incomplete block designs (BIBDs), resolvable balanced incomplete block designs (RBIBDs), and the corresponding resolutions. In particular, three algorithms for isomorphfree exhaustive generation of (v, k, λ)BIBDs and resolutions are described and applied to settle existence and classification problems. The first algorithm generates BIBDs point by point using an orderly algorithm in combination with a maximum clique algorithm. The second and third algorithm generate resolutions of BIBDs by utilizing a correspondence between resolutions and certain optimal qary errorcorrecting codes. The second algorithm generates the corresponding codes codeword by codeword, and is analogous in structure to the first algorithm. The third algorithm generates codes coordinate by coordinate, and is based on the recent isomorphfree exhaustive generation framework of Brendan McKay. The main result of this report is a proof of nonexistence for a (15, 5, 4)
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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Cited by 2 (1 self)
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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.
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.
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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Cited by 1 (1 self)
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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.
Lehrstuhl II für Mathematik (Informatik)
, 2003
"... 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 hi ..."
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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 at highest flexibility in using constraints during the generation process and, thus, meeting the needs of practical applications.
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
projective Hjelmslev planes over chain rings of order 25
"... Abstract. In this paper a 2arc of size 21 in the projective Hjelmslev plane PHG(2,Z25) and a 2arc of size 22 in PHG(2,F5[X]/(X2)) are given. Both arcs are bigger than the 2arcs previously known in the respective plane. Furthermore, we will give some information on the geometrical structure of the ..."
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Abstract. In this paper a 2arc of size 21 in the projective Hjelmslev plane PHG(2,Z25) and a 2arc of size 22 in PHG(2,F5[X]/(X2)) are given. Both arcs are bigger than the 2arcs previously known in the respective plane. Furthermore, we will give some information on the geometrical structure of the arcs. 1