**Contemporary Mathematics**

Volume: 452;
2008;
187 pp;
Softcover

MSC: Primary 52;
Secondary 05; 11; 13; 14; 90

Print ISBN: 978-0-8218-4173-0

Product Code: CONM/452

List Price: $65.00

AMS Member Price: $52.00

MAA Member Price: $58.50

**Electronic ISBN: 978-0-8218-8131-6
Product Code: CONM/452.E**

List Price: $65.00

AMS Member Price: $52.00

MAA Member Price: $58.50

# Integer Points in Polyhedra—Geometry, Number Theory, Representation Theory, Algebra, Optimization, Statistics

Share this page *Edited by *
*Matthias Beck; Christian Haase; Bruce Reznick; Michèle Vergne; Volkmar Welker; Ruriko Yoshida*

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

## Integer Points in Polyhedra -- Geometry, Number Theory, Representation Theory, Algebra, Optimization, Statistics

- Contents v6 free
- Preface vii8 free
- List of Participants ix10 free
- Lattice reformulation of integer programming problems 114 free
- Local Euler-Maclaurin expansion of Barvinok valuations and Ehrhart coefficients of a rational polytope 1528
- Combinatorial aspects of mirror symmetry 3548
- Ehrhart polynomial roots and Stanley's non-negativity theorem 6780
- Enumeration of integer solutions to linear inequalities defined by digraphs 7992
- Perfect Delaunay polytopes and perfect quadratic functions on lattices 93106
- Quasi-period collapse and GLn(Z)-scissors congruence in rational polytopes 115128
- Quadratic Gröbner bases arising from combinatorics 123136
- Ehrhart analogue of the h-vector 139152
- Saturation points on faces of a rational polyhedral cone 147160
- An explicit formulation for two dimensional vector partition functions 163176
- Let me tell you my favorite lattice-point problem … 179192