discipline 
Pure Math

subject 
Symmetric
combinatorial structures

lecturers 
Tamás Szőnyi, Péter Sziklai, András Gács 
credits 
2 
period 
1, 3 
curriculum 
Projective and affine planes, Latin squares. Planes over a field and their representations. t(v,k,l) designs. Restrictions on the parameters. Fisher's inequalty (for t=2). Skew intersecting systems, square designs. Linear algebra methods. Some more nonexistence results: the BruckRyserChowla theorem and its variants. Problems concerning the existence of projective planes. Characterization of the design of points and hyperplanes of a projective space (DembowskiWagner); the parameters do not characterize the design (Kantor). Biplanes (lambda=2), Hadamard matrices and designs (t=2). Some examples, Paley design, PG(n1,2). Strongly regular graphs: restrictions on the parameters. The pointgraph of designs and strongly regular graphs. “Switching” of strongly regular graphs (Seidel). Examples: ladder graph and triangular graph, etc. Recursive construction of designs: point and blockresidual design, extension. Hadamard 3designs, extension of affine planes (inversive planes). Extension of projective planes and symmetric designs in general (Cameron's theorem). Sketch of construction of the Witt designs for the Matieu groups. Asymptotic results for the existence of designs (Wilson's theorem, Teirlinck's theorem for the existence of designs with t>5 without proof). Difference sets and Hall's multiplyer theorem. 
literature 
CameronVan Lint:
Designs, graphs, codes and their links, 
form of tuition 
lectures 
mode of assessment 
Oral exam 