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Geometric Combinatorics
 
Edited by: Ezra Miller University of Minnesota, Minneapolis, MN
Victor Reiner University of Minnesota, Minneapolis, MN
Bernd Sturmfels University of California, Berkeley, Berkeley, CA
A co-publication of the AMS and IAS/Park City Mathematics Institute
Geometric Combinatorics
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
Geometric Combinatorics
Click above image for expanded view
Geometric Combinatorics
Edited by: Ezra Miller University of Minnesota, Minneapolis, MN
Victor Reiner University of Minnesota, Minneapolis, MN
Bernd Sturmfels University of California, Berkeley, Berkeley, CA
A co-publication of the AMS and IAS/Park City Mathematics Institute
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
  • Book Details
     
     
    IAS/Park City Mathematics Series
    Volume: 132007; 691 pp
    MSC: 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.

    Readership

    Graduate students and research mathematicians interested in combinatorics; discrete methods in geometry and topology.

  • Table of Contents
     
     
    • 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
  • Reviews
     
     
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 132007; 691 pp
MSC: 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.

Readership

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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.