Description

Book Synopsis
Presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. This book starts with the basics of polytope theory. It introduces Schlegel and Gale diagrams as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in 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.

Lectures in Geometric Combinatorics

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A Paperback by Rekha R. Thomas

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    View other formats and editions of Lectures in Geometric Combinatorics by Rekha R. Thomas

    Publisher: MP-AMM American Mathematical
    Publication Date: 6/30/2006 12:00:00 AM
    ISBN13: 9780821841402, 978-0821841402
    ISBN10: 0821841408
    Also in:
    Combinatorics and graph theory Discrete mathematics

    Description

    Book Synopsis
    Presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. This book starts with the basics of polytope theory. It introduces Schlegel and Gale diagrams as geometric tools to visualize polytopes in high dimension and to unearth bizarre phenomena in 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.

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