Applied Geometry and Discrete Mathematics: The Victor Klee Festschrift

Front Cover
Peter Gritzmann, Bernd Sturmfels, Victor Klee
American Mathematical Soc. - Mathematics - 608 pages
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This volume, published jointly with the Association for Computing Machinery, comprises a collection of research articles celebrating the occasion of Victor Klee's 65th birthday in September 1990. During his long career, Klee has made contributions to a wide variety of areas, such as discrete and computational geometry, convexity, combinatorics, graph theory, functional analysis, mathematical programming and optimization, and theoretical computer science. In addition, Klee made important contributions to mathematics, education, mathematical methods in economics and the decision sciences, applications of discrete mathematics in the biological and social sciences, and the transfer of knowledge from applied mathematics to industry. In honour of Klee's achievements, this volume presents more than 40 papers on topics related to Klee's research. While the majority of the papers are research articles, a number of survey articles are also included. Mirroring the breadth of Klee's mathematical contributions, this book shows how different branches of mathematics interact. It is a fitting tribute to one of the leading figures in discrete mathematics.
 

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Contents

Selfduality Groups and Ranks of Selfdualities
11
Do Projections Go to Infinity?
51
The Minimal Projective Plane Polyhedral Maps
63
Packing Euclidean Space with Congruent Cylinders
71
Extended EulerPoincare Relations for Cell Complexes
81
Computing the Convex Hull in the Euclidean Plane
91
Measures of FStars in Finitely Starlike Sets
109
On SignNonsingular Matrices and the Conversion
117
Volume Approximation of Convex Bodies by Circumscribed Polytopes
309
Points Sets with Small Integral Distances
319
Convex Minimizers of Variational Problems
325
Flattening a Rooted Tree
335
Every Tree is Graceful But Some are More Graceful than Others
355
Centers and Invariant Points of Convex Bodies
367
The Diameter of Graphs of Convex Polytopes and Vector Theory
387
Multiply Perspective Simplices Desmic Triads
413

Recognizing Properties of Periodic Graphs
135
Some Regular Maps and Their Polyhedral Realizations
157
Volumes of a Random Polytope in a Convex
175
Bodies of Constant Width in Riemannian Manifolds
181
Uniquely Remotal Hulls
193
The Symmetries of the Cut Polytope and of Some Relatives
205
Complete Descriptions of Small Multicut Polytopes
221
A Hyperplane Incidence Problem with Applications
253
Gaps in Difference Sets and the Graph of Nearly Equal Distances
265
Remarks on 5Neighbor Packings and Coverings with Circles
275
Symmetric Solutions to Isoperimetric Problems for Polytopes
289
A Global Newton Method
301
Submanifolds of the Cube
423
Finite Unions of Closed Subgroups of the Dimensional Torus
433
Regular Triangulations of Convex Polytopes
443
On the Number of Antipodal or Strictly Antipodal Pairs
457
MultiOrder Convexity
471
Almost Orthogonal Lines in
489
Exact Upper Bounds for the Number of Faces in dDimensional
517
Stretchability of Pseudolines is NPHard
531
A Zonotope Associated with Graphical Degree Sequences
555
The Combinatorics of Bivariate Splines
587
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