Contents

Preface vii

List of Participants ix

Lattice reformulation of integer programming problems

KAREN AARDAL

1

Local Euler-Maclaurin expansion of Barvinok valuations and Ehrhart

coefficients of a rational polytope

VELLEDA BALDONI, NICOLE BERLINE, and MICHELE VERGNE 15

Combinatorial aspects of mirror symmetry

VICTOR BATYREV and BENJAMIN NILL 35

Ehrhart polynomial roots and Stanley's non-negativity theorem

BENJAMIN BRAUN and MIKE DEVELIN 67

Enumeration of integer solutions to linear inequalities defined by digraphs

J.

WILLIAM DAVIS, ERWIN D'SOUZA, SUNYOUNG LEE,

and CARLA D. SAVAGE 79

Perfect Delaunay polytopes and perfect quadratic functions on lattices

ROBERT ERDAHL, ANDREI 0RDINE, and KONSTANTIN RYBNIKOV 93

Quasi-period collapse and GLn(Z)-scissors congruence in rational polytopes

CHRISTIAN HAASE and TYRRELL B. McALLISTER 115

Quadratic Grobner bases arising from combinatorics

TAKAYUKI HIBI and HIDEFUMI 0HSUGI 123

Ehrhart analogue of the h-vector

KALLE KARU 139

Saturation points on faces of a rational polyhedral cone

AKIMICHI TAKEMURA AND RURIKO YOSHIDA 147

An explicit formulation for two dimensional vector partition functions

ZHIQIANG Xu 163

Let me tell you my favorite lattice-point problem ...

MATTHIAS BECK and BRUCE REZNICK (EDITORS) 179

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