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A Construction of Isomorphism Classes of Oriented Matroids

In: Algorithmic Algebraic Combinatorics and Gröbner Bases

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  • Ralf Gugisch

    (University of Bayreuth, Mathematisches Institut)

Abstract

Summary We developed a computer program for generating all oriented matroids corresponding to a prescribed underlying matroid. The generation process and its output can be controlled via a variety of possible restrictions allowing to generate specific sets of oriented matroids. The tool was mainly intended for application in chemistry: According to an idea of A. Dreiding and A. Dress, oriented matroid generation may be used as a first step towards a conformation generation for chemical structures. We describe the main ideas of the generation algorithm as well as an application to the conformation analysis of cyclohexane. A combination with the Gröbner base approach for conformation analysis going back to P. Hazebroek and L. Oosterhoff is suggested.

Suggested Citation

  • Ralf Gugisch, 2009. "A Construction of Isomorphism Classes of Oriented Matroids," Springer Books, in: Mikhail Klin & Gareth A. Jones & Aleksandar Jurišić & Mikhail Muzychuk & Ilia Ponomarenko (ed.), Algorithmic Algebraic Combinatorics and Gröbner Bases, pages 229-249, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-01960-9_7
    DOI: 10.1007/978-3-642-01960-9_7
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