Titlebook: Algorithmic Algebraic Combinatorics and Gröbner Bases; Mikhail Klin,Gareth A. Jones,Ilia Ponomarenko Book 2009 Springer-Verlag Berlin Heid

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https://doi.org/10.1007/978-3-658-06532-4In the study of finite geometries one often requires knowledge of the ranks of related (0,1)-incidence matrices. We describe some of the combinatorial questions in finite geometry for which formulas for these ranks are useful; and we describe methods from algebraic geometry that are useful in obtaining such rank formulas.

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https://doi.org/10.1007/978-3-319-25757-0In this chapter we introduce the notion of total graph coherent configuration, and use computer tools to investigate it for two classes of strongly regular graphs – the triangular graphs .(.) and the lattice square graphs ..(.). For .(.), we show that its total graph coherent configuration has exceptional mergings only in the cases .=5 and .=7.

integral

Using Gröbner Bases to Investigate Flag Algebras and Association Scheme FusionThis paper is meant primarily as a . on how to phrase problems in association schemes in the language of Gröbner bases and use the computational results provided by those bases, though it does contain fusion scheme computations not previously found in the literature.

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A Construction of Designs from ,(2,,) and ,(2,,), ,=1 mod 6, on ,+2 PointsLet .=.(2,.) or .(2,.). We consider the action of . on the projective line together with one additional point, which is fixed by .. Assume .≡1 mod 6 and set.We construct .designs admitting .(2,.) as their automorphisms, if .≡3 mod 4. We also construct .designs admitting .(2,.) as their automorphisms. These designs may not be simple.

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Algorithmic Algebraic Combinatorics and Gröbner Bases

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