Horizons of Combinatorics (Bolyai Society Mathematical Studies (17))

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. 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. Ervin Győri, Gyula O.h. Katona, László Lovász (eds.). Based On Papers Presented At The Conference Horizons Of Combinatorics During The Period July 17-21, 2006 At Balatonalmádi (lake Balaton, Hungary)--pref. Includes Bibliographical References. Front Matter....Pages 1-8 Ballot Theorems, Old and New....Pages 9-35 Statistical Inference on Random Structures....Pages 37-66 Proof Techniques for Factor Theorems....Pages 67-78 Erdős-Hajnal-type Results on Intersection Patterns of Geometric Objects....Pages 79-103 Old and New Problems and Results in Ramsey Theory....Pages 105-118 Forbidden Intersection Patterns in the Families of Subsets (Introducing a Method)....Pages 119-140 Subsums of a Finite Sum and Extremal Sets of Vertices of the Hypercube....Pages 141-161 Combinatorial Conditions for the Rigidity of Tensegrity Frameworks....Pages 163-177 Polygonal Graphs....Pages 179-188 Infinite Combinatorics: From Finite to Infinite....Pages 189-213 The Random Walk Method for Intersecting Families....Pages 215-234 Problems and Results on Colorings of Mixed Hypergraphs....Pages 235-255 Random Discrete Matrices....Pages 257-280 Hungarian mathematics has always been known for discrete mathematics, including combinatorial number theory, set theory and recently random structures, and 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