Abstract
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.
Original language | English |
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Pages (from-to) | 394-437 |
Number of pages | 44 |
Journal | Australasian Journal of Combinatorics |
Volume | 67 |
Issue number | 2 |
State | Published - 1 Jan 2017 |
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics