Algebraic combinatorics on convex polytopes:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Glebe, Australia
Carslaw Publ.
1992
|
| Series: | Carslaw mathematics texts
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 164 S. |
| ISBN: | 1875399046 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804123387122941952 |
|---|---|
| adam_text | PART ONE Face Numbers
of Simplicial Complexes
I Convex Polytopes
and Simplicial Complexes 1
1. Convex Polytopes 1
2. Faces 3
3. Polyhedral Complexes 7
4. Simplicial Complexes 8
5. Face Posets 10
6. / Vectors and /i Vectors 12
II Kruskal Katona
Theorem 15
7. Binomial Representations 15
8. Reverse Lexicographic Order 17
9. / Vectors of
Simplicial Complexes 18
III Simplicial Polytopes
and Spheres 23
10. Simplicial Spheres 23
11. Dehn Sommerville Equations 24
12. Upper Bound Conjecture 25
13. Lower Bound Theorem 29
IV O Sequences and
Cohen—Macaulay Rings 31
14. Graded Algebras 31
15. Hilbert Functions
and Hilbert Series 33
16. Krull Dimensions and
Systems of Parameters 34
17. Cohen Macaulay Rings 37
18. O Sequences (or M Vectors) 38
V Stanley s Result on the
Upper Bound Conjecture 41
19. Face Rings
of Simplicial Complexes 41
20. Stanley s Idea 44
VI Reisner s Topological
Criterion 47
21. Reduced Simplicial
Homology Groups 47
22. Reisner s Theorem 51
VII Cohen—Macaulay
Complexes 55
23. Cohen Macaulay
and Shellable Complexes 55
24. Subcomplexes of
Cohen Macaulay Complexes 60
VIII Buchsbaum Simplicial
Complexes 63
25. Betti Number Sequences 63
26. Buchsbaum Complexes 64
PART TWO Ehrhart Polyno¬
mials of Convex Polytopes
IX Ehrhart s
Fundamental Results 71
27. Simplicial Cones Associated
with Simplices 71
28. Ehrhart Polynomials 77
29. Ehrhart s Law of Reciprocity 81
30. Some Examples 83
X Hochster s Theorem 87
31. Rational Convex
Polyhedral Cones 87
32. Noether Normalization
Lemma (General Form) 91
33. Hochster s Theorem 95
XI Combinatorics
on £—Sequences 101
34. Review of ^ Sequences 101
35. Dual Polytopes
and Symmetric ^ Sequences 103
36. Lower Bound Theorem
And Upper Bound Theorem 110
PART THREE Algebras with
Straightening Laws
XII Cohen—Macaulay
Partially Ordered Sets 115 .
37. Posets and Lattices 115
38. Cohen Macaulay Posets 119
XIII Algebras with Straight¬
ening Laws 123
39. Definition and Examples
of ASL s 123
40. Fundamental Theorem
on ASL s 128
41. Integral Posets and
Distributive Lattices 129
XIV / and h Vectors
of Simplicial Posets 135
42. Simplicial Posets 135
43. / Vectors of
Simplicial Posets 137
44. h Vectors of Cohen—Macaulay
Simplicial Posets 139
XV Hodge Algebras 143
45. Definition of Hodge Algebras 143
46. Existence of Hodge
Algebra Structures 145
Appendices 153
A. Hilbert Basis Theorem 153
B. Noether Normalization Lemma 155
References 157
Index 161
|
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| classification_rvk | SK 170 |
| ctrlnum | (OCoLC)29023080 (DE-599)BVBBV009033643 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV009033643 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:28:57Z |
| institution | BVB |
| isbn | 1875399046 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005976477 |
| oclc_num | 29023080 |
| open_access_boolean | |
| owner | DE-29T |
| owner_facet | DE-29T |
| physical | 164 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Carslaw Publ. |
| record_format | marc |
| series2 | Carslaw mathematics texts |
| spelling | Hibi, Takayuki Verfasser (DE-588)138393648 aut Algebraic combinatorics on convex polytopes Takayuki Hibi Glebe, Australia Carslaw Publ. 1992 164 S. txt rdacontent n rdamedia nc rdacarrier Carslaw mathematics texts Combinatorial analysis Complexes Convex polytopes Konvexes Polytop (DE-588)4367579-7 gnd rswk-swf Kombinatorische Analysis (DE-588)4164746-4 gnd rswk-swf Kombinatorische Analysis (DE-588)4164746-4 s Konvexes Polytop (DE-588)4367579-7 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005976477&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hibi, Takayuki Algebraic combinatorics on convex polytopes Combinatorial analysis Complexes Convex polytopes Konvexes Polytop (DE-588)4367579-7 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd |
| subject_GND | (DE-588)4367579-7 (DE-588)4164746-4 |
| title | Algebraic combinatorics on convex polytopes |
| title_auth | Algebraic combinatorics on convex polytopes |
| title_exact_search | Algebraic combinatorics on convex polytopes |
| title_full | Algebraic combinatorics on convex polytopes Takayuki Hibi |
| title_fullStr | Algebraic combinatorics on convex polytopes Takayuki Hibi |
| title_full_unstemmed | Algebraic combinatorics on convex polytopes Takayuki Hibi |
| title_short | Algebraic combinatorics on convex polytopes |
| title_sort | algebraic combinatorics on convex polytopes |
| topic | Combinatorial analysis Complexes Convex polytopes Konvexes Polytop (DE-588)4367579-7 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd |
| topic_facet | Combinatorial analysis Complexes Convex polytopes Konvexes Polytop Kombinatorische Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005976477&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hibitakayuki algebraiccombinatoricsonconvexpolytopes |