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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.

Algebra --- Mathematics --- Physical Sciences & Mathematics --- Combinatorial analysis. --- Combinatorics --- Mathematical analysis --- Combinatorics. --- Discrete groups. --- Differentiable dynamical systems. --- Functional analysis. --- Genetics --- Convex and Discrete Geometry. --- Dynamical Systems and Ergodic Theory. --- Functional Analysis. --- Genetics and Population Dynamics. --- Mathematics. --- Biology --- Embryology --- Mendel's law --- Adaptation (Biology) --- Breeding --- Chromosomes --- Heredity --- Mutation (Biology) --- Variation (Biology) --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Groups, Discrete --- Infinite groups --- Discrete mathematics --- Convex geometry . --- Discrete geometry. --- Dynamics. --- Ergodic theory. --- Biomathematics. --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Geometry --- Combinatorial geometry --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics)