Facing up to arrangements: face-count formulas for partitions of space by hyperplanes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
1975
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| Schriftenreihe: | American Mathematical Society: Memoirs of the American Mathematical Society
154 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Volume 1, Issue 1, Number 154 (first of 2 numbers) |
| Beschreibung: | VII, 102 S. |
| ISBN: | 0821818546 |
Internformat
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| 245 | 1 | 0 | |a Facing up to arrangements: face-count formulas for partitions of space by hyperplanes |c Thomas Zaslavsky |
| 264 | 1 | |a Providence, RI |c 1975 | |
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| 490 | 1 | |a American Mathematical Society: Memoirs of the American Mathematical Society |v 154 | |
| 500 | |a Volume 1, Issue 1, Number 154 (first of 2 numbers) | ||
| 502 | |a Zugl.: Cambridge, Univ., Diss., 1974 | ||
| 650 | 7 | |a Combinatoire |2 fourier | |
| 650 | 4 | |a Géométrie combinatoire | |
| 650 | 7 | |a Géométrie |2 fourier | |
| 650 | 4 | |a Problèmes combinatoires d'énumération | |
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Datensatz im Suchindex
| _version_ | 1804117355901485056 |
|---|---|
| adam_text | TABLE OF CONTENTS
Section Page
0. Introduction to arrangements 1
PART I. HOW TO COUNT THE FACES OF AN ARRANGEMENT OF HYPERPLANES 9
1. First facts about arrangements 10
A. The lattice and rank of an arrangement. 10
B. The lattice and the geometry of an arrangement. 11
C. The Mobius function and two latticial polynomials. 12
D. Direct sum, induced arrangement, projectivization. 14
2. The main theorems. 18
A. The Euclidean case. 18
Theorem A.
B. The projective case. 20
Theorem B.
C. The bounded case. 21
Theorem C.
D. Relative vertices and cross sections of Euclidean 27
arrangements.
3. Quick proofs (Eulerian method) 30
AB. Proof of the whole space cases. 31
C. The bounded case and the bounded space. 32
4. The long proofs (Tutte Grothendieck method) 37
A. Proof of the Euclidean case. 38
B. Proof of the projective case. 42
C. Proof of the bounded case. 44
5. A collocation of corollaries 53
A. The Euler relations proved. 53
B. More counting relations. 55
C. Enumeration in the classical style. 57
v
D. Unbounded faces. 61
E. Back to Buck: arrangements made simple. 64
F. Winder s Theorem and threshold functions. 67
6. Points and zonotopes. .................... 71
A. Placing hyperplanes between points. 71
B. The faces of zonotopes. 72
PART II. A STUDY OF EUCLIDEAN ARRANGEMENTS WITH PARTICULAR 75
REFERENCE TO BOUNDED FACES
7. The beta theorem 76
Theorem D.
8. The central decomposition 80
Theorem E.
A. Appendix on spanning sets of coatoms. 86
9. The dimension of the bounded space. 94
References 97
Index of symbols. ... ............... 100
|
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| discipline | Mathematik |
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| isbn | 0821818546 |
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| spelling | Zaslavsky, Thomas Verfasser aut Facing up to arrangements: face-count formulas for partitions of space by hyperplanes Thomas Zaslavsky Providence, RI 1975 VII, 102 S. txt rdacontent n rdamedia nc rdacarrier American Mathematical Society: Memoirs of the American Mathematical Society 154 Volume 1, Issue 1, Number 154 (first of 2 numbers) Zugl.: Cambridge, Univ., Diss., 1974 Combinatoire fourier Géométrie combinatoire Géométrie fourier Problèmes combinatoires d'énumération Treillis, Théorie des Hyperebene (DE-588)4161050-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Hyperebene (DE-588)4161050-7 s DE-604 Erscheint auch als Online-Ausgabe 978-0-8218-9955-7 American Mathematical Society: Memoirs of the American Mathematical Society 154 (DE-604)BV008000141 154 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001922446&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zaslavsky, Thomas Facing up to arrangements: face-count formulas for partitions of space by hyperplanes American Mathematical Society: Memoirs of the American Mathematical Society Combinatoire fourier Géométrie combinatoire Géométrie fourier Problèmes combinatoires d'énumération Treillis, Théorie des Hyperebene (DE-588)4161050-7 gnd |
| subject_GND | (DE-588)4161050-7 (DE-588)4113937-9 |
| title | Facing up to arrangements: face-count formulas for partitions of space by hyperplanes |
| title_auth | Facing up to arrangements: face-count formulas for partitions of space by hyperplanes |
| title_exact_search | Facing up to arrangements: face-count formulas for partitions of space by hyperplanes |
| title_full | Facing up to arrangements: face-count formulas for partitions of space by hyperplanes Thomas Zaslavsky |
| title_fullStr | Facing up to arrangements: face-count formulas for partitions of space by hyperplanes Thomas Zaslavsky |
| title_full_unstemmed | Facing up to arrangements: face-count formulas for partitions of space by hyperplanes Thomas Zaslavsky |
| title_short | Facing up to arrangements: face-count formulas for partitions of space by hyperplanes |
| title_sort | facing up to arrangements face count formulas for partitions of space by hyperplanes |
| topic | Combinatoire fourier Géométrie combinatoire Géométrie fourier Problèmes combinatoires d'énumération Treillis, Théorie des Hyperebene (DE-588)4161050-7 gnd |
| topic_facet | Combinatoire Géométrie combinatoire Géométrie Problèmes combinatoires d'énumération Treillis, Théorie des Hyperebene Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001922446&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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