Hardcover ISBN: | 978-0-8218-3736-8 |
Product Code: | PCMS/13 |
List Price: | $125.00 |
MAA Member Price: | $112.50 |
AMS Member Price: | $100.00 |
eBook ISBN: | 978-1-4704-3912-5 |
Product Code: | PCMS/13.E |
List Price: | $112.00 |
MAA Member Price: | $100.80 |
AMS Member Price: | $89.60 |
Hardcover ISBN: | 978-0-8218-3736-8 |
eBook: ISBN: | 978-1-4704-3912-5 |
Product Code: | PCMS/13.B |
List Price: | $237.00 $181.00 |
MAA Member Price: | $213.30 $162.90 |
AMS Member Price: | $189.60 $144.80 |
Hardcover ISBN: | 978-0-8218-3736-8 |
Product Code: | PCMS/13 |
List Price: | $125.00 |
MAA Member Price: | $112.50 |
AMS Member Price: | $100.00 |
eBook ISBN: | 978-1-4704-3912-5 |
Product Code: | PCMS/13.E |
List Price: | $112.00 |
MAA Member Price: | $100.80 |
AMS Member Price: | $89.60 |
Hardcover ISBN: | 978-0-8218-3736-8 |
eBook ISBN: | 978-1-4704-3912-5 |
Product Code: | PCMS/13.B |
List Price: | $237.00 $181.00 |
MAA Member Price: | $213.30 $162.90 |
AMS Member Price: | $189.60 $144.80 |
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Book DetailsIAS/Park City Mathematics SeriesVolume: 13; 2007; 691 ppMSC: Primary 05; 52; Secondary 06; 14; 57
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.
Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute.
ReadershipGraduate students and research mathematicians interested in combinatorics; discrete methods in geometry and topology.
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Table of Contents
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Chapters
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What is geometric combinatorics?—An overview of the graduate summer school
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Lattice points, polyhedra, and complexity
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Root systems and generalized associahedra
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Topics in combinatorial differential topology and geometry
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Geometry of $q$ and $q,t$-analogs in combinatorial enumeration
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Chromatic numbers, morphism complexes, and Stiefel-Whitney characteristic classes
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Equivariant invariants and linear geometry
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An introduction to hyperplane arrangements
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Poset topology: Tools and applications
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Convex polytopes: Extremal constructions and $f$-vector shapes
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Reviews
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The editors have done an excellent job in bringing together many leaders of the field and encouraging them to write expository lecture notes on various topics that expertly showcase the multi-faceted world of this vast and rapidly growing field of mathematics.
MAA Reviews
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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
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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.
Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute.
Graduate students and research mathematicians interested in combinatorics; discrete methods in geometry and topology.
-
Chapters
-
What is geometric combinatorics?—An overview of the graduate summer school
-
Lattice points, polyhedra, and complexity
-
Root systems and generalized associahedra
-
Topics in combinatorial differential topology and geometry
-
Geometry of $q$ and $q,t$-analogs in combinatorial enumeration
-
Chromatic numbers, morphism complexes, and Stiefel-Whitney characteristic classes
-
Equivariant invariants and linear geometry
-
An introduction to hyperplane arrangements
-
Poset topology: Tools and applications
-
Convex polytopes: Extremal constructions and $f$-vector shapes
-
The editors have done an excellent job in bringing together many leaders of the field and encouraging them to write expository lecture notes on various topics that expertly showcase the multi-faceted world of this vast and rapidly growing field of mathematics.
MAA Reviews