Hungarian mathematics has always been known for discrete mathematics, including combinatorial number theory, set theory and recently random structures, combinatorial geometry as well.

The recent volume contains high level surveys on these topics with authors mostly being invited speakers for the conference "Horizons of Combinatorics" held in Balatonalmadi, Hungary in 2006. The collection gives a very good overview of recent trends and results in a large part of combinatorics and related topics, and offers an interesting reading for experienced specialists as well as to young researchers and students.

Autorentext
László Lovász ist einer der Leiter der theoretischen Forschungsabteilung der Microsoft Corporation. Er hat 1999 den Wolf-Preis sowie den Gödel-Preis für die beste wissenschaftliche Veröffentlichung in der Informatik erhalten.

Inhalt
Ballot Theorems, Old and New.- Statistical Inference on Random Structures.- Proof Techniques for Factor Theorems.- Erd?s-Hajnal-type Results on Intersection Patterns of Geometric Objects.- Old and New Problems and Results in Ramsey Theory.- Forbidden Intersection Patterns in the Families of Subsets (Introducing a Method).- Subsums of a Finite Sum and Extremal Sets of Vertices of the Hypercube.- Combinatorial Conditions for the Rigidity of Tensegrity Frameworks.- Polygonal Graphs.- Infinite Combinatorics: From Finite to Infinite.- The Random Walk Method for Intersecting Families.- Problems and Results on Colorings of Mixed Hypergraphs.- Random Discrete Matrices.