Recent Trends in Combinatorics

✍ Scribed by Andrew Beveridge, Jerrold R. Griggs, Leslie Hogben, Gregg Musiker, Prasad Tetali (eds.)

• Publisher: Springer
• Year: 2016
• Tongue: English
• Leaves: 775
• Series: IMA volumes in mathematics and its applications 159
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xiii
Front Matter....Pages 1-1
Problems related to graph indices in trees....Pages 3-30
The edit distance in graphs: Methods, results, and generalizations....Pages 31-62
Repetitions in graphs and sequences....Pages 63-81
Extremal problems for cycles in graphs....Pages 83-116
A survey of Turán problems for expansions....Pages 117-143
Recent advances on Dirac-type problems for hypergraphs....Pages 145-165
Rainbow Hamilton cycles in random graphs and hypergraphs....Pages 167-189
Further applications of the Container Method....Pages 191-213
Independent transversals and hypergraph matchings - an elementary approach....Pages 215-233
Giant components in random graphs....Pages 235-256
Infinite random graphs and properties of metrics....Pages 257-273
Nordhaus-Gaddum problems for Colin de Verdière type parameters, variants of tree-width, and related parameters....Pages 275-294
Algebraic aspects of the normalized Laplacian....Pages 295-315
Progress on poset-free families of subsets....Pages 317-338
The mathematics of causal sets....Pages 339-365
Front Matter....Pages 367-367
Lectures on approximate groups and Hilbert’s 5th problem....Pages 369-404
Character sums and arithmetic combinatorics....Pages 405-417
Sum-product formulae....Pages 419-451
Ajtai–Szemerédi Theorems over quasirandom groups....Pages 453-484
Front Matter....Pages 485-485
Some algorithmic applications of partition functions in combinatorics....Pages 487-509
Front Matter....Pages 485-485
Partition analysis, modular functions, and computer algebra....Pages 511-543
Moments of orthogonal polynomials and combinatorics....Pages 545-578
The combinatorics of knot invariants arising from the study of Macdonald polynomials....Pages 579-600
A survey of consecutive patterns in permutations....Pages 601-618
Dynamical algebraic combinatorics and the homomesy phenomenon....Pages 619-652
Face enumeration on simplicial complexes....Pages 653-686
Unimodality problems in Ehrhart theory....Pages 687-711
Simplicial and cellular trees....Pages 713-752
Parametric polyhedra with at least k lattice points: Their semigroup structure and the k-Frobenius problem....Pages 753-778

✦ Subjects

Analyse combinatoire