21-25 August 2012
Portorož, Slovenia
UTC timezone
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Constructive classification of strongly regular designs

Presented by Dr. Sven REICHARD
Type: Oral presentation

Content

Coherent configurations (Higman, Weisfeiler-Leman) are a central notion in Algebraic Graph Theory. An important class of coherent configurations - the so-called Schurian configurations - are obtained from the 2-orbits of permutation groups of finite degree. However in general, coherent configurations are non-Schurian. Important invariants of coherent configurations are their types; they include information on the number and sizes of the fibers, which are the combinatorial analogues of the simplest characteristics for the orbits of permutation groups. Configurations with a single fiber are known as association schemes, and they have been studied extensively, leading to complete catalogues for moderately small orders (Hanaki-Miyamoto). This is in contrast to the situation of coherent configurations in general. Until recently, no such catalogues existed even for the smallest orders. Recently we started first attempts towards the systematical enumeration of small coherent configurations. In this presentation we restrict ourselves to a particular class of two-fiber configurations, namely strongly regular designs (Higman). (We extend Higman's definition by removing a rather artificial condition, namely that the graphs induced on each fiber be primitive.) We propose a strategy for their enumeration and present our results, which in particular include a complete list of such designs with at most 24 points and blocks.We also give computer-free models of a few newly discovered designs, as well as new descriptions of some classical objects like Reye's configuration and 24-cell. Keywords: Coherent configuration, strongly regular graph, equitable partition, exhaustive search

Place

Location: Portorož, Slovenia
Address: University of Primorska, Faculty of Tourism Studies, Obala 11a, SI-6320 Portorož - Portorose, Slovenia
Room: VP1

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