Lectures in Geometric Combinatorics

Rekha R. Thomas, "Lectures in Geometric Combinatorics"
Amer Mathematical Society | July 31, 2006 | English | ISBN: 0821841408 | 143 pages | File type: PDF | 1 mb

This book presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. The book starts with the basics of polytope theory. Schlegel and Gale diagrams are introduced as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in polytopes. The heart of the book is a treatment of the secondary polytope of a point configuration and its connections to the state polytope of the toric ideal defined by the configuration. These polytopes are relatively recent constructs with numerous connections to discrete geometry, classical algebraic geometry, symplectic geometry, and combinatorics.

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