Next Meeting

Topics:

Cliques in the half cube graph and not-Pascal's triangle Richard Green University of Colorado at Boulder The half cube graph is the graph whose vertices can be identified a set of 2n-1 vertices of the n-dimensional hypercube that are at mutually even Hamming distance. Two vertices are connected by an edge if and only if the corresponding points are at Hamming distance 2. Not-Pascal's triangle is a seemingly nameless Pascal-like triangle that appears in various contexts. We will discuss the combinatorics of cliques in the half cube graph, their relationship with the aforementioned triangle, and much more.

Generalized quadrangles and Singer groups Stefaan DeWinter Ghent University, Belguim Several people have wondered as to whether it is possible to develop a Singer group theory for other geometries than projective planes. D. Ghinelli initiated such theory for GQs, and a question of J.C. Fisher motivated E.E. Shult, K.Thas and myself to further study GQs admitting a Singer group. In this talk I will report on work we have done during a Research in Pairs stay at Oberwolfach last year. Our main result shows that among all known GQs and all hypothetical GQs that might be constructed using a known construction method only one speciic class admits a Singer group. This provides further strong evidence for a conjecture we formulated earlier on GQs with a Singer group.