Softcover ISBN:  9780821841730 
Product Code:  CONM/452 
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MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
Electronic ISBN:  9780821881316 
Product Code:  CONM/452.E 
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Book DetailsContemporary MathematicsVolume: 452; 2008; 187 ppMSC: Primary 52; Secondary 05; 11; 13; 14; 90;
The AMSIMSSIAM 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 latticepoint 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.ReadershipGraduate 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 EulerMaclaurin 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 nonnegativity 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  Quasiperiod 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 latticepoint problem $\dots $ [ MR 2405772 ]


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The AMSIMSSIAM 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 latticepoint 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.
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 EulerMaclaurin 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 nonnegativity 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  Quasiperiod 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 latticepoint problem $\dots $ [ MR 2405772 ]