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We introduce the notion of the combinatorial extension of a Terwilliger algebra by a coherent algebra. By using this notion, we find a simple way to describe the Terwilliger algebras of certain coherent configurations as combinatorial extensions of simpler Terwilliger algebras. In particular, given an association scheme S and another association scheme R such that the Terwilliger algebra of R...
In this paper, we give a new class of association schemes whose thin residues are isomorphic to an elementary abelian p -group of order p 2 . We then study the automorphism groups of these schemes and determine whether these schemes are schurian.
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