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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
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