**Contemporary Mathematics**

Volume: 374;
2005;
191 pp;
Softcover

MSC: Primary 52;
Secondary 05; 11; 13; 14; 62; 68; 90

Print ISBN: 978-0-8218-3459-6

Product Code: CONM/374

List Price: $69.00

Individual Member Price: $55.20

**Electronic ISBN: 978-0-8218-7964-1
Product Code: CONM/374.E**

List Price: $69.00

Individual Member Price: $55.20

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

Share this page *Edited by *
*Alexander Barvinok; Matthias Beck; Christian Haase; Bruce Reznick; Volkmar Welker*

The AMS-IMS-SIAM Summer Research Conference on Integer Points in Polyhedra took place in Snowbird (UT). This proceedings volume contains original research and survey articles stemming from that event. Topics covered include commutative algebra, optimization, discrete geometry, statistics, representation theory, and symplectic geometry. The book is suitable for researchers and graduate students interested in combinatorial aspects of the above fields.

#### Table of Contents

# Table of Contents

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

- Contents v6 free
- Preface vii8 free
- List of Participants ix10 free
- A weighted version of quantization commutes with reduction for a toric manifold 114 free
- Coefficients and roots of Ehrhart polynomials 1528
- Ehrhart polynomials of lattice polyhedral functions 3750
- Lattice points, contingency tables, and sampling 6578
- Kostka numbers and Littlewood-Richardson coefficients 7992
- Polar decomposition and Brion's theorem 91104
- Gröbner basis degree bounds on Tor·k[Λ](k, k)· and discrete Morse theory for posets 101114
- Integer programming, duality and superadditive functions 139152
- The Cayley trick and triangulations of products of simplices 151164
- Problems from the Cottonwood Room 179192
- Questions about Ehrhart coefficients. 180193
- A conjecture about the Euler characteristic of algebraic varieties over the fields Fq, R, C and the division ring H. 181194
- Lattice points in homogeneously expanding compact domains. 182195
- Reflexive polytopes in dimension 2 and 3, and the numbers 12 and 24. 184197
- Are smooth toric ideals quadratically generated? 186199
- The classification of 1-point lattice tetrahedra. 187200
- A conjecture on lattice tiles. 189202
- Covering minima, free planes and deep holes 190203

#### Readership

Graduate students and research mathematicians interested in combinatorics.