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Tue, 15 Apr 2008 11:07:00 +0200Tue, 15 Apr 2008 11:07:00 +0200Integral point sets over Z_n^m
http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/377
There are many papers studying properties of point sets in the Euclidean space or on integer grids, with pairwise integral or rational distances. In this article we consider the distances or coordinates of the point sets which instead of being integers are elements of Z_n, and study the properties of the resulting combinatorial structures.Axel Kohnert; Sascha Kurzpreprinthttp://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/377Tue, 15 Apr 2008 11:07:00 +0200Symmetric functions in MAGMA
http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/267
We describe two algorithms which were used to implement symmetric functions in the computer algebra system MAGMA. We describe one algorithm based on the work of Lascoux and Schutzenberger for the multiplication. One further algorithm is given for the computation of plethysms.Axel Kohnertarticlehttp://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/267Wed, 04 Jul 2007 07:49:22 +0200A note on Erdös-Diophantine graphs and Diophantine carpets
http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/177
A Diophantine figure is a set of points on the integer grid $\mathbb{Z}^{2}$ where all mutual Euclidean distances are integers. We also speak of Diophantine graphs. The vertices are points in $\mathbb{Z}^{2}$ (the coordinates)and the edges are labeled with the distance between the two adjacent vertices, which is integral. In this language a Diophantine figure is a complete Diophantine graph. Two Diophantine graphs are equivalent if they only differ by translation or rotation of vertices. Due to a famous theorem of Erdös and Anning there are complete Diophantine graphs which are not contained in larger ones. We call them Erdös-Diophantine graphs. A special class of Diophantine graphs are Diophantine carpets. These are planar triangulations of a subset of the integer grid. We give an effective construction for Erdös-Diophantine graphs and characterize the chromatic number of Diophantine carpets.Axel Kohnert; Sascha Kurzpreprinthttp://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/177Wed, 07 Dec 2005 14:56:57 +0100Construction of Two-Weight Codes
http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/174
This is a talk given at the conference: Algebra and Computation 2005 in Tokyo. We describe a method for the construction of two-weight codes. This also allows to realize certain strongly regular graphs or equivalently certain point sets in the a finite projective geometry. We use the method of prescibed automorphisms, which allows us to reduce the problem to a size where we can use powerful Diophantine equation solvers provided by Alfred Wassermann.Axel Kohnertarticlehttp://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/174Mon, 05 Dec 2005 08:42:29 +0100