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arXiv · 1010.4450

On quasi-thin association schemes

M. Muzychuk·I. Ponomarenko
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Abstract

An association scheme is called quasi-thin if the valency of each its basic relation is one or two. A quasi-thin scheme is Kleinian if the thin residue of it forms a Klein group with respect to the relation product. It is proved that any Kleinian scheme arises from near-pencil on~$3$ points, or affine or projective plane of order~$2$. The main result is that any non-Kleinian quasi-thin scheme a) is the two-orbit scheme of a suitable permutation group, and b) is characterized up to isomorphism by its intersection number array. An infinite family of Kleinian quasi-thin schemes for which neither a) nor b) holds is also constructed.

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M. Muzychuk, I. Ponomarenko. 2010-10-21. On quasi-thin association schemes. https://arxiv.org/abs/1010.4450

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