Recent Trends in Combinatorics

1. Front Matter

   Pages i-xiii

   PDF

2. Extremal and Probabilistic Combinatorics

   1. Front Matter

      Pages 1-1

      PDF

   2. Problems related to graph indices in trees

      • László Székely, Stephan Wagner, Hua Wang

      Pages 3-30

   3. The edit distance in graphs: Methods, results, and generalizations

      • Ryan R. Martin

      Pages 31-62

   4. Repetitions in graphs and sequences

      • Maria Axenovich

      Pages 63-81

   5. Extremal problems for cycles in graphs

      • Jacques Verstraëte

      Pages 83-116

   6. A survey of Turán problems for expansions

      • Dhruv Mubayi, Jacques Verstraëte

      Pages 117-143

   7. Recent advances on Dirac-type problems for hypergraphs

      • Yi Zhao

      Pages 145-165

   8. Rainbow Hamilton cycles in random graphs and hypergraphs

      • Asaf Ferber, Michael Krivelevich

      Pages 167-189

   9. Further applications of the Container Method

      • József Balogh, Adam Zsolt Wagner

      Pages 191-213

   10. Independent transversals and hypergraph matchings - an elementary approach

       • Penny Haxell

       Pages 215-233

   11. Giant components in random graphs

       • Mihyun Kang

       Pages 235-256

   12. Infinite random graphs and properties of metrics

       • Anthony Bonato, Jeannette Janssen

       Pages 257-273

   13. Nordhaus-Gaddum problems for Colin de Verdière type parameters, variants of tree-width, and related parameters

       • Leslie Hogben

       Pages 275-294

   14. Algebraic aspects of the normalized Laplacian

       • Steve Butler

       Pages 295-315

   15. Progress on poset-free families of subsets

       • Jerrold R. Griggs, Wei-Tian Li

       Pages 317-338

   16. The mathematics of causal sets

       • Graham Brightwell, Malwina Luczak

       Pages 339-365

3. Additive and Analytic Combinatorics

   1. Front Matter

      Pages 367-367

      PDF

   2. Lectures on approximate groups and Hilbert’s 5th problem

      • Emmanuel Breuillard

      Pages 369-404

   3. Character sums and arithmetic combinatorics

      • Mei-Chu Chang

      Pages 405-417

This volume presents some of the research topics discussed at the 2014-2015 Annual Thematic Program Discrete Structures: Analysis and Applications at the Institute for Mathematics and its Applications during Fall 2014, when  combinatorics was the focus. Leading experts have written surveys of research problems, making state of the art results more conveniently and widely available. The three-part structure of the volume reflects the three workshops held during Fall 2014. In the first part, topics on extremal and probabilistic combinatorics are presented; part two focuses on additive and analytic combinatorics; and part three presents topics in geometric and enumerative combinatorics. This book will be of use to those who research combinatorics directly or apply combinatorial methods to other fields.

• Cominatorics
• Discrete Dynamical Systems
• Discrete Geometry
• Enumerative Cominatorics
• Hamilton Cycles
• Probabilistic Combinatorics
• Turan Problems
• Graph theory
• Extremal Combinatorics
• Additive Combinatorics
• Analytic Combinatorics
• Geometric Combinatorics
• Posets
• Spectral graph theory
• Combinatorial matrix theory
• combinatorics

• Dept of Math, Statistics & Comp.Sc, Macalester College, St. Paul, USA

  Andrew Beveridge

• Dept. of Mathematics, University of South Carolina, Columbia, USA

  Jerrold R. Griggs

• Dept. of Mathematics, Iowa State University, Ames, USA

  Leslie Hogben

• School of Mathematics, University of Minnesota, Minneapolis, USA

  Gregg Musiker

• School of Mathematics & Computer Sc, Georgia Institute of Technology, Atlanta, USA

  Prasad Tetali

Policies and ethics