Lectures on polytopes

著者

• Ziegler, Gunter M

書誌事項

Lectures on polytopes

Günter M. Ziegler

（Graduate texts in mathematics, 152）

Springer-Verlag, c2006

Updated 7th printing of 1st ed.

• : pbk.
• : hdk.

注記

Bibliography: p. [325]-366

Includes index

内容説明・目次

巻冊次

: hdk. ISBN 9780387943299

内容説明

Based on a graduate course at the Technische Universitat, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The straightforward exposition features many illustrations, and complete proofs for most theorems. With only linear algebra as a prerequisite, it takes the reader quickly from the basics to topics of recent research. The lectures introduce basic facts about polytopes, with an emphasis on methods that yield the results, discuss important examples and elegant constructions, and show the excitement of current work in the field. They will provide interesting and enjoyable reading for researchers as well as students.

目次

and Examples.- Polytopes, Polyhedra, and Cones.- Faces of Polytopes.- Graphs of Polytopes.- Steinitz’ Theorem for 3-Polytopes.- Schlegel Diagrams for 4-Polytopes.- Duality, Gale Diagrams, and Applications.- Fans, Arrangements, Zonotopes, and Tilings.- Shellability and the Upper Bound Theorem.- Fiber Polytopes, and Beyond.- Fiber Polytopes, and Beyond.

巻冊次

: pbk. ISBN 9780387943657

内容説明

Based on a graduate course at the Technische Universitat, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The straightforward exposition features many illustrations, and complete proofs for most theorems. With only linear algebra as a prerequisite, it takes the reader quickly from the basics to topics of recent research. The lectures introduce basic facts about polytopes, with an emphasis on methods that yield the results, discuss important examples and elegant constructions, and show the excitement of current work in the field. They will provide interesting and enjoyable reading for researchers as well as students.

目次

• Preface
• Preface to the Second Printing
• Introduction and Examples
• 1. Polytopes, Polyhedra, and Cones
• 2. Faces of Polytopes
• 3. Graphs for Polytopes
• 4. Steinitz' Theorem for 3-Polytopes
• 5. Schlegel Diagrams for 4-Polytopes
• 6. Duality, Gale Diagrams, and Applications
• 7. Fans, Arrangements, Zonotopes, and Tilings
• 8. Shellability and the Upper Bound Theorem
• 9. Fiber Polytopes, and Beyond
• References
• Index.

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BA8573684X
• ISBN:
  • 9780387943657
  • 0387943293
• LCCN: 94021784
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: New York
• ページ数/冊数: xiii, 373 p.
• 大きさ: 24 cm
• 分類:
  • LCC : QA691
  • DC20 : 516.3/5
  • NDC8 : 411.8
• 件名:
  • LCSH : Polytopes
• 親書誌ID:
  • BA00010074