University of Delaware
Discrete Mathematics Seminar

New infinite families of non-Schurian association schemes of order 2p²
Misha Klin
Ben Gurion University, Israel
Tuesday, October 2, 2012
Ewing Hall 336 4.00 - 5.00 pm

ABSTRACT:

Joint with Stefan Gyurki.

Association schemes form one of the traditional areas of investigations in algebraic graph theory. Catalogues of all small association schemes for a good decade are available from the website of Hanaki and Miyamoto. It is known that all association schemes of order up to 14 are Schurian, that is they are coming from suitable transitive permutation groups in the standard manner. First examples of non-Schurian association schemes exist on 15, 16 and 18 vertices. In particular, there are just two examples of non-Schurian association schemes of order 18.

Starting from successful computer free interpretation of these two examples, and using extensive computer algebra experimentation in conjunction with further lucky plausible reasonings, we were able to observe the existence of at least four infinite families of non-Schurian association schemes of order 2p² (for p prime, p>3).

In this lecture I will start from the consideration of the two starting examples on 18 points, will describe some auxiliary coherent configurations, after that four infinite families of association schemes will be presented. We will discuss some of their properties, as well as their links with certain known objects in extremal graph theory.