SUBJECT
Title
Combinatorial geometry
Type of instruction
lecture + practical
Level
master
Faculty
Part of degree program
Credits
2+2
Recommended in
Semesters 1-4
Typically offered in
Autumn/Spring semester
Course description
- Combinatorial properties of finite projective and affine spaces. Collineations and polarities, conics, quadrics, Hermitian varieties, circle geometries, generalized quadrangles.
- Point sets with special properties in Euclidean spaces. Convexity, Helly-type theorems, transversals.
- Polytopes in Euclidean, hyperbolic and spherical geometries. Tilings, packings and coverings. Density problems, systems of circles and spheres.
Readings
- Boltyanski, V., Martini, H. and Soltan, P.S.: Excursions into Combinatorial Geometry, Springer-Verlag, Berlin-Heidelberg-New York, 1997.
- Coxeter, H.S.M.: Introduction to Geometry, John Wiley & Sons, New York, 1969.
- Fejes Tóth L.: Regular Figures, Pergamon Press, Oxford-London-New York-Paris, 1964.