Algorithmic Approach to Non-symmetric 3-class Association Schemes

Leif K. Jørgensen ()
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Leif K. Jørgensen: Aalborg University, Department of Mathematical Sciences

A chapter in Algorithmic Algebraic Combinatorics and Gröbner Bases, 2009, pp 251-268 from Springer

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.

Keywords: Association schemes; Orientation of strongly regular graphs; Computer search (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-01960-9_8

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DOI: 10.1007/978-3-642-01960-9_8

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