Lectures in geometric combinatorics
Author(s)
Bibliographic Information
Lectures in geometric combinatorics
（Student mathematical library, v. 33 . IAS/Park City mathematical subseries）
American Mathematical Society , Institute for Advanced Study, c2006
- Other Title
-
STML/IAS/PARK CITY 33
Available at / 32 libraries
-
No Libraries matched.
- Remove all filters.
Note
Includes bibliographical references (p. 139-140) and index
Description and Table of Contents
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 Grobner 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.
Table of Contents
Abstract algebra: Groups, rings and fields Convex polytopes: Definitions and examples Faces of polytopes Schlegel diagrams Gale diagrams Bizarre polytopes Triangulations of point configurations The secondary polytope The permutahedron Abstract algebra: Polynomial rings Grobner bases I Grobner bases II Initial complexes of toric ideals State polytopes of toric ideals Bibliography Index.
by "Nielsen BookData"
