SUBJECT

Discrete geometry

lecture + practical

master

Faculty of Science

Mathematics MSc

4+3

Semesters 1-4

Autumn/Spring semester

Packings and coverings in E2. Dowker theorems. The theorems of L. Fejes Tóth and Rogers on densest packing of translates of a convex or centrally symmetric convex body. Homogeneity questions. Lattice-like arrangements. Homogeneous packings (with group actions). Space claim, separability.

Packings and coverings in (Euclidean, hyperbolic or spherical space) Ad. Problems with the definition of density. Densest circle packings (spaciousness), and thinnest circle coverings in A2. Tammes problem. Solidity. Rogers’ density bound for sphere packings in Ed. Clouds, stable systems and separability. Densest sphere packings in A3. Tightness and edge tightness. Finite systems. Problems about common transversals.

1. Fejes Tóth, L.: Regular figures, Pergamon Press, Oxford–London–New York–Paris, 1964.
2. Fejes Tóth, L.: Lagerungen in der Ebene auf der Kugel und im Raum, Springer-Verlag,
3. Berlin–Heidelberg–NewYork, 1972.
4. Rogers, C. A.:  Packing and covering, Cambridge University Press, 1964.
5. Böröczky, K. Jr.:  Finite packing and covering, Cambridge Ubiversity Press, 2004.