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Algorithmic Approach to Non-symmetric 3-class Association Schemes

In: Algorithmic Algebraic Combinatorics and Gröbner Bases

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  • Leif K. Jørgensen

    (Aalborg University, Department of Mathematical Sciences)

Abstract

Summary There are 24 feasible parameter sets for a primitive non-symmetric association schemes with 3 classes and at most 100 vertices. Using computer search, we prove non-existence for three feasible parameter sets. Ten cases are still open. In the imprimitive case, we survey the known results including some constructions of infinite families of schemes. In the smallest case that has been open up to now, we use computer search to find new schemes. These schemes are equivalent to “skew” Bush-type Hadamard matrices of order 36. We also consider directed graphs that satisfy only some of the conditions required for a non-symmetric association scheme with 3 classes.

Suggested Citation

  • Leif K. Jørgensen, 2009. "Algorithmic Approach to Non-symmetric 3-class Association Schemes," Springer Books, in: Mikhail Klin & Gareth A. Jones & Aleksandar Jurišić & Mikhail Muzychuk & Ilia Ponomarenko (ed.), Algorithmic Algebraic Combinatorics and Gröbner Bases, pages 251-268, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-01960-9_8
    DOI: 10.1007/978-3-642-01960-9_8
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