Lectures in Geometric Combinatorics
( Student Mathematical Library )
Publication series ：Student Mathematical Library
Author： Rekha R. Thomas
Publisher： American Mathematical Society
Publication year： 2006
E-ISBN: 9781470421441
P-ISBN(Paperback): 9780821841402
Subject： O18 geometric topology
Keyword： Discrete Mathematics and Combinatorics
Language： ENG
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Lectures in Geometric Combinatorics
Description
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. The connections rely on Gröbner bases of toric ideals and other methods from commutative algebra. The book is self-contained and does not require any background beyond basic linear algebra. With numerous figures and exercises, it can be used as a textbook for courses on geometric, combinatorial, and computational aspects of the theory of polytopes.
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