Lectures in Geometric Combinatorics pdf epub mobi txt 电子书下载 2025

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出版者:Amer Mathematical Society

作者:Rekha R. Thomas

出品人:

页数:143

译者:

出版时间:2006-7-31

价格:USD 29.00

装帧:Paperback

isbn号码:9780821841402

丛书系列:Student Mathematical Library

图书标签:

数学
Mathematics
Geometry
Combinatorics
计算机科学
组合
科普
in
几何组合学
组合数学
离散几何
图论
代数组合学
凸几何
排列组合
数学
高等教育
学术著作

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具体描述

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.

作者简介

Rekha R. Thomas: University of Washington, Seattle, WA

目录信息

Cover 1
Title 2
Copyright 3
Contents 4
IAS /Park City Mathematics Institute 6
Preface 8
Chapter 1. Abstract Algebra: Groups, Rings and Fields 10
Chapter 2. Convex Polytopes: Definitions and Examples 16
Chapter 3. Faces of Polytopes 24
Chapter 4. Schlegel Diagrams 34
Chapter 5. Gale Diagrams 46
Chapter 6. Bizarre Polytopes 56
Chapter 7. Triangulations of Point Configurations 66
Chapter 8. The Secondary Poly tope 82
Chapter 9. The Permutahedron 94
Chapter 10. Abstract Algebra: Polynomial Rings 102
Chapter 11. Grobner Bases I 110
Chapter 12. Grobner Bases II 120
Chapter 13. Initial Complexes of Toric Ideals 126
Chapter 14. State Polytopes of Toric Ideals 136
Bibliography 148
Index 150
A 150
B 150
C 150
D 150
E 150
F 150
G 151
H 151
I 151
L 151
M 151
N 151
O 151
P 151
R 152
S 152
T 152
U 152
V 152
Z 152
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