Let p be an odd prime. We provide a construction of four non-Schurian association schemes for every prime p ≥ 5 and two for p = 3. For p > 3 the construction is new, while for p = 3 it coincides with the non- Schurian schemes, obtained with the aid of a computer by A. Hanaki and I. Miyamoto. The discovered non-Schurian objects appear as algebraic mergings of the Schurian coherent configuration on 2p2 points and rank 6p−2, which corresponds to the action of the Heisenberg group of order p3 on the set of points and lines of the classical biaffine plane. The results obtained are considered in a wider framework.
|Number of pages||44|
|Journal||Australasian Journal of Combinatorics|
|State||Published - 1 Jan 2017|