Geometric combinatorics describes a wide area of mathematics that is primarily the study of geometric objects and their combinatorial structure. Perhaps the most familiar examples are polytopes and simplicial complexes, but the subject is much broader. This volume is a compilation of expository articles at the interface between combinatorics and geometry, based on a three-week program of lectures at the Institute for Advanced Study/Park City Math Institute (IAS/PCMI) summer program on Geometric Combinatorics.The topics covered include posets, graphs, hyperplane arrangements, discrete Morse theory, and more. These objects are considered from multiple perspectives, such as in enumerative or topological contexts, or in the presence of discrete or continuous group actions. Most of the exposition is aimed at graduate students or researchers learning the material for the first time. Many of the articles include substantial numbers of exercises, and all include numerous examples. The reader is led quickly to the state of the art and current active research by worldwide authorities on their respective subjects.Information for our distributors: Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

Richard Stanley's work in combinatorics revolutionized and reshaped the subject. Many of his hallmark ideas and techniques imported from other areas of mathematics have become mainstays in the framework of modern combinatorics. In addition to collecting several of Stanley's most influential papers, this volume also includes his own short reminiscences on his early years, and on his celebrated proof of The Upper Bound Theorem.

Richard Stanley's work in combinatorics revolutionized and reshaped the subject, inspiring a generation of researchers, through his lectures, papers, and books. In this volume, these researchers explain how Stanley's vision and insights influenced and guided their own perspectives on the subject. As a valuable bonus, this book contains a collection of Stanley's short comments on each of his papers.This book may serve as an introduction to several different threads of ongoing research in combinatorics as well as giving historical perspective.

Geometric combinatorics describes a wide area of mathematics that is primarily the study of geometric objects and their combinatorial structure. Perhaps the most familiar examples are polytopes and simplicial complexes, but the subject is much broader. This volume is a compilation of expository articles at the interface between combinatorics and geometry, based on a three-week program of lectures at the Institute for Advanced Study/Park City Math Institute (IAS/PCMI) summer program on Geometric Combinatorics.The topics covered include posets, graphs, hyperplane arrangements, discrete Morse theory, and more. These objects are considered from multiple perspectives, such as in enumerative or topological contexts, or in the presence of discrete or continuous group actions. Most of the exposition is aimed at graduate students or researchers learning the material for the first time. Many of the articles include substantial numbers of exercises, and all include numerous examples. The reader is led quickly to the state of the art and current active research by worldwide authorities on their respective subjects.Information for our distributors: Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

Richard Stanley's work in combinatorics revolutionized and reshaped the subject. Many of his hallmark ideas and techniques imported from other areas of mathematics have become mainstays in the framework of modern combinatorics. In addition to collecting several of Stanley's most influential papers, this volume also includes his own short reminiscences on his early years, and on his celebrated proof of The Upper Bound Theorem.

Richard Stanley's work in combinatorics revolutionized and reshaped the subject, inspiring a generation of researchers, through his lectures, papers, and books. In this volume, these researchers explain how Stanley's vision and insights influenced and guided their own perspectives on the subject. As a valuable bonus, this book contains a collection of Stanley's short comments on each of his papers.This book may serve as an introduction to several different threads of ongoing research in combinatorics as well as giving historical perspective.