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Facing up to arrangements: face-count formulas for partitions of space by hyperplanes

About this Title

Thomas Zaslavsky

Publication: Memoirs of the American Mathematical Society
Publication Year: 1975; Volume 1, Number 154
ISBNs: 978-0-8218-1854-1 (print); 978-0-8218-9955-7 (online)
DOI: https://doi.org/10.1090/memo/0154
MathSciNet review: 0357135

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Table of Contents

Chapters

  • Introduction to arrangements
  • Part I. How to count the faces of an arrangement of hyperplanes
  • 1. First facts about arrangements
  • 2. The main theorems
  • 3. Quick proofs (Eulerian method)
  • 4. The long proofs (Tutte–Grothendieck method)
  • 5. A collocation of corollaries
  • 6. Points and zonotopes
  • Part II. A study of Euclidean arrangements with particular reference to bounded faces
  • 7. The beta theorem
  • 8. The central decomposition
  • 9. The dimension of the bounded space