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.