Seminár z teórie grafov - Michail Klin (27.4.2017)

vo štvrtok 27.4.2017 o 9:50 hod. v miestnosti M/213

---

Prednášajúci: Michail Klin (Ben Gurion University, Beer Sheva, Israel)

Názov: Constructive enumeration of some classes of coherent configurations: an attempt at a brief survey

Termín: 27.4.2017, 9:50 hod., M/213

Abstrakt:
We report about recent results, related to constructive enumeration (up to isomorphism) of some classes of coherent configurations (CC). Computer aided techniques, used by younger colleagues, goes back to the traditions of Soviet school, and in particular to Igor A.Faradzev. Special attention is payed to so-called non-Schurian objects, those, which are not related to the centralizer algebra of a suitable permutation group. For a long while the smallest known non-Schurian objects were on 15, 16 and 18 points. Non-Schurian doubly regular tornament on 15 points, due to Dima Pasechnik, will be mentioned.

At the beginning, enumeration of small strongly regular designs (SRDs), in the sense of Donald Higman, will be briefly discussed, basing on the results of MK with Sven Reichard.

The cantral part of the talk will be related to the enumeration of all CCs on up to 15 points (MZA). The main consequence of this enumeration is that all CCs on up to 13 points are Schurian. There exists exactly one new rank 11 non-Schurian CC M with two fibres on 14 points. There are two non_Schurian CCs on 15 points. A friendly computer free interpretation of the new CC M will be given in terms of an SRD with 8 vertices and 6 blocks.

If time will allow, a history of enumeration of Schur rings over groups of order up to 64 will be considered, with special emphasis on results by MZA and Sven Reichard.

---