Some new non-schurian association schemes on 2p2 points, p an odd prime, and related combinatorial structures

Štefan Gyürki, Mikhail Klin

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)394-437
Number of pages44
JournalAustralasian Journal of Combinatorics
Volume67
Issue number2
StatePublished - 1 Jan 2017

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