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Integer Points in Polyhedra—Geometry, Number Theory, Representation Theory, Algebra, Optimization, Statistics
 
Edited by: Matthias Beck San Francisco State University, San Francisco, CA
Christian Haase Freie Universität Berlin, Berlin, Germany
Bruce Reznick University of Illinois at Urbana-Champaign, Urbana, IL
Michèle Vergne Ecole Polytechnique, Palaiseau, France
Volkmar Welker Phillips-Universität Marburg, Marburg, Germany
Ruriko Yoshida University of Kentucky, Lexington, KY
Integer Points in Polyhedra---Geometry, Number Theory, Representation Theory, Algebra, Optimization,Statistics
Softcover ISBN:  978-0-8218-4173-0
Product Code:  CONM/452
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-8131-6
Product Code:  CONM/452.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-4173-0
eBook: ISBN:  978-0-8218-8131-6
Product Code:  CONM/452.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
Integer Points in Polyhedra---Geometry, Number Theory, Representation Theory, Algebra, Optimization,Statistics
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Integer Points in Polyhedra—Geometry, Number Theory, Representation Theory, Algebra, Optimization, Statistics
Edited by: Matthias Beck San Francisco State University, San Francisco, CA
Christian Haase Freie Universität Berlin, Berlin, Germany
Bruce Reznick University of Illinois at Urbana-Champaign, Urbana, IL
Michèle Vergne Ecole Polytechnique, Palaiseau, France
Volkmar Welker Phillips-Universität Marburg, Marburg, Germany
Ruriko Yoshida University of Kentucky, Lexington, KY
Softcover ISBN:  978-0-8218-4173-0
Product Code:  CONM/452
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-8131-6
Product Code:  CONM/452.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-4173-0
eBook ISBN:  978-0-8218-8131-6
Product Code:  CONM/452.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 4522008; 187 pp
    MSC: Primary 52; Secondary 05; 11; 13; 14; 90;

    The AMS-IMS-SIAM Joint Summer Research Conference “Integer Points in Polyhedra—Geometry, Number Theory, Representation Theory, Algebra, Optimization, Statistics” was held in Snowbird, Utah in June 2006. This proceedings volume contains research and survey articles originating from the conference.

    The volume is a cross section of recent advances connected to lattice-point questions. Similar to the talks given at the conference, topics range from commutative algebra to optimization, from discrete geometry to statistics, from mirror symmetry to geometry of numbers. The book is suitable for researchers and graduate students interested in combinatorial aspects of the above fields.

    Readership

    Graduate students and research mathematicians interested in combinatorics and its applications.

  • Table of Contents
     
     
    • Articles
    • Karen Aardal — Lattice reformulation of integer programming problems [ MR 2405761 ]
    • Velleda Baldoni, Nicole Berline and Michèle Vergne — Local Euler-Maclaurin expansion of Barvinok valuations and Ehrhart coefficients of a rational polytope [ MR 2405762 ]
    • Victor Batyrev and Benjamin Nill — Combinatorial aspects of mirror symmetry [ MR 2405763 ]
    • Benjamin Braun and Mike Develin — Ehrhart polynomial roots and Stanley’s non-negativity theorem [ MR 2405764 ]
    • J. William Davis, Erwin D’Souza, Sunyoung Lee and Carla D. Savage — Enumeration of integer solutions to linear inequalities defined by digraphs [ MR 2405765 ]
    • Robert Erdahl, Andrei Ordine and Konstantin Rybnikov — Perfect Delaunay polytopes and perfect quadratic functions on lattices [ MR 2405766 ]
    • Christian Haase and Tyrrell B. McAllister — Quasi-period collapse and ${\rm GL}_n(\Bbb Z)$-scissors congruence in rational polytopes [ MR 2405767 ]
    • Hidefumi Ohsugi and Takayuki Hibi — Quadratic Gröbner bases arising from combinatorics [ MR 2405768 ]
    • Kalle Karu — Ehrhart analogue of the $h$-vector [ MR 2405769 ]
    • Akimichi Takemura and Ruriko Yoshida — Saturation points on faces of a rational polyhedral cone [ MR 2405770 ]
    • Zhiqiang Xu — An explicit formulation for two dimensional vector partition functions [ MR 2405771 ]
    • Matthias Beck, Benjamin Nill, Bruce Reznick, Carla Savage, Ivan Soprunov and Zhiqiang Xu — Let me tell you my favorite lattice-point problem $\dots $ [ MR 2405772 ]
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 4522008; 187 pp
MSC: Primary 52; Secondary 05; 11; 13; 14; 90;

The AMS-IMS-SIAM Joint Summer Research Conference “Integer Points in Polyhedra—Geometry, Number Theory, Representation Theory, Algebra, Optimization, Statistics” was held in Snowbird, Utah in June 2006. This proceedings volume contains research and survey articles originating from the conference.

The volume is a cross section of recent advances connected to lattice-point questions. Similar to the talks given at the conference, topics range from commutative algebra to optimization, from discrete geometry to statistics, from mirror symmetry to geometry of numbers. The book is suitable for researchers and graduate students interested in combinatorial aspects of the above fields.

Readership

Graduate students and research mathematicians interested in combinatorics and its applications.

  • Articles
  • Karen Aardal — Lattice reformulation of integer programming problems [ MR 2405761 ]
  • Velleda Baldoni, Nicole Berline and Michèle Vergne — Local Euler-Maclaurin expansion of Barvinok valuations and Ehrhart coefficients of a rational polytope [ MR 2405762 ]
  • Victor Batyrev and Benjamin Nill — Combinatorial aspects of mirror symmetry [ MR 2405763 ]
  • Benjamin Braun and Mike Develin — Ehrhart polynomial roots and Stanley’s non-negativity theorem [ MR 2405764 ]
  • J. William Davis, Erwin D’Souza, Sunyoung Lee and Carla D. Savage — Enumeration of integer solutions to linear inequalities defined by digraphs [ MR 2405765 ]
  • Robert Erdahl, Andrei Ordine and Konstantin Rybnikov — Perfect Delaunay polytopes and perfect quadratic functions on lattices [ MR 2405766 ]
  • Christian Haase and Tyrrell B. McAllister — Quasi-period collapse and ${\rm GL}_n(\Bbb Z)$-scissors congruence in rational polytopes [ MR 2405767 ]
  • Hidefumi Ohsugi and Takayuki Hibi — Quadratic Gröbner bases arising from combinatorics [ MR 2405768 ]
  • Kalle Karu — Ehrhart analogue of the $h$-vector [ MR 2405769 ]
  • Akimichi Takemura and Ruriko Yoshida — Saturation points on faces of a rational polyhedral cone [ MR 2405770 ]
  • Zhiqiang Xu — An explicit formulation for two dimensional vector partition functions [ MR 2405771 ]
  • Matthias Beck, Benjamin Nill, Bruce Reznick, Carla Savage, Ivan Soprunov and Zhiqiang Xu — Let me tell you my favorite lattice-point problem $\dots $ [ MR 2405772 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.