Construction of finite structures

Construction of finite structures

Construction of finite structures is a scientific project supported by the Fonds zur Förderung der wissenschaftlichen Forschung. It has the project number P10189 - PHY. H. Fripertinger works in this project under the supervision of Prof. J. Schwaiger. Most of the scientific work is done in cooperation with Lehrstuhl II für Mathematik of the university of Bayreuth.

This project is dealing with various methods of Algebraic Combinatorics. In other words combinatorial algorithms are discussed for the enumeration and construction of essentially different objects (called orbits) under a (finite) group action. Some more information in German is available:

• Description of this project.
• Report of the activities in 1995.
• Report of the activities in 1996.
• Request for prolongation of this research project.
• The final report gives a complete overview over all activities during the last years.

Some of the main results of this project on applications of these methods to the enumeration of linear codes, endofunction and on applications in musical theory and chemistry can be found in the following list:

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• Isometry Classes of Indecomposable Linear Codes
• Zyklenzeiger linearer Gruppen und Abzählung linearer Codes
• Cycle indices of linear, affine and projective groups
• Endofunctions of given cycle type
• Enumeration of mosaics
• The Cycle Index of the Symmetry Group of the Fullerene C₆₀
• The 3-dimensional Cycle Index of the Leapfrog of a Polyhedron
• Enumeration, construction and random generation of block codes
• Regular connected matroids

GDPR

Construction of finite structures