Recent Trends in Combinatorics (eBook)

Section 1: Extremal and Probabilistic Combinatorics.- Problems Related to Graph Indices in Trees.- The edit distance in graphs: methods, results and generalizations.- Repetitions in graphs and sequences.- On Some Extremal Problems for Cycles in Graphs.- A survey of Turan problems for expansions.- Survey on matching, packing and Hamilton cycle problems on hypergraphs.- Rainbow Hamilton cycles in random graphs and hypergraphs.- Further applications of the Container Method.- Independent transversals and hypergraph matchings - an elementary approach.- Giant components in random graphs.- Infinite random graphs and properties of metrics.- Nordhaus-Gaddum Problems for Colin de Verdière Type Parameters, Variants of Tree-width, and Related Parameters.- Algebraic aspects of the normalized Laplacian.- Poset-free Families of Subsets.- Mathematics of causal sets.- Section 2: Additive and Analytic Combinatorics.- Lectures on Approximate groups and Hilbert's 5th Problem.- Character sums and arithmetic combinatorics.- On sum-product problem.- Ajtai-Szemerédi Theorems over quasirandom groups.- Section 3: Enumerative and Geometric Combinatorics.- Moments of orthogonal polynomials and combinatorics.- The combinatorics of knot invariants arising from the study of Macdonald polynomials.- Some algorithmic applications of partition functions in combinatorics.- Partition Analysis, Modular Functions, and Computer Algebra.- A survey of consecutive patterns in permutations.- Unimodality Problems in Ehrhart Theory.- Face enumeration on simplicial complexes.- Simplicial and Cellular Trees.- Parametric Polyhedra with at least k Lattice Points: Their Semigroup Structure and the k-Frobenius Problem.- Dynamical Algebraic Combinatorics and the Homomesy Phenomenon.