Oriented matroids

Anders Björner ... [et al.]

Oriented matroids are a very natural mathematical concept which presents itself in many different guises and which has connections and applications to many different areas. These include discrete and computational geometry, combinatorics, convexity, topology, algebraic geometry, operations research, computer science and theoretical chemistry. This is the second edition of the first comprehensive, accessible account of the subject. It is intended for a diverse audience: graduate students who wish to learn the subject from scratch; researchers in the various fields of application who want to concentrate on certain aspects of the theory; specialists who need a thorough reference work; and others at academic points in between. A list of exercises and open problems ends each chapter. For the second edition, the authors have expanded the bibliography greatly to ensure that it remains comprehensive and up-to-date, and they have also added an appendix surveying research since the work was first published.

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[目次]

  • Preface
  • Notation
  • 1. A first orientation session
  • 2. A second orientation session
  • 3. Axiomatics
  • 4. From face lattices to topology
  • 5. Topological models for oriented matroids
  • 6. Arrangements of pseudolines
  • 7. Constructions
  • 8. Realizability
  • 9. Convex polytopes
  • 10. Linear programming
  • Appendix: Some current frontiers of research
  • Bibliography
  • Index.

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この本の情報

書名 Oriented matroids
著作者等 Björner, Anders
Doran B.
Ismail M.
Lam T. Y.
Rota G.-C.
Sturmfels Bernd
Vergnas Michel Las (Laboratoire de Probabilites Universite Pierre et Marie Curie)
White Neil
Wutwak E.
Ziegler Glnter M. (Technische Universitat Berlin)
Bjorner Anders
シリーズ名 Encyclopedia of mathematics and its applications
出版元 Cambridge University Press
刊行年月 1999
版表示 2nd ed
ページ数 xii, 548 p.
大きさ 24 cm
ISBN 9780521777506
NCID BA44601307
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言語 英語
出版国 イギリス
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