Computational oriented matroids: equivalence classes of matrices within a natural framework
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2006
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Publisher description Table of contents only Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 314-321) and index |
| Physical Description: | XIII, 323 S. Ill., graph. Darst. |
| ISBN: | 9780521849302 0521849306 |
Staff View
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| 245 | 1 | 0 | |a Computational oriented matroids |b equivalence classes of matrices within a natural framework |c Jürgen G. Bokowski |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2006 | |
| 300 | |a XIII, 323 S. |b Ill., graph. Darst. | ||
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| 500 | |a Includes bibliographical references (p. 314-321) and index | ||
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Record in the Search Index
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| adam_text | COMPUTATIONAL ORIENTED MATROIDS EQUIVALENCE CLASSES OF MATRICES WITHIN A
NATURAL FRAMEWORK JURGEN G. BOKOWSKI DARMSTADT UNIVERSITY OF TECHNOLOGY
GERMANY CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE PAGE XI 1 GEOMETRIC
MATRIX MODELS I 1 1.1 A CONVEX POLYTOPE 4 1.2 A VECTOR CONFIGURATION 10
1.3 A CHIROTOPE, ORIENTATIONS OF ALL SIMPLICES 14 1.4 A CENTRAL
HYPERPLANE CONFIGURATION 17 1.5 A GREAT-SPHERE ARRANGEMENT 18 1.6 A SET
OF HYPERLINE SEQUENCES 19 1.7 A POINT SET ON A SPHERE 25 1.8 A SIGNED
AFFINE POINT SET 25 1.9 A SET OF ORIENTED AFFINE HYPERPLANES 27 1.10 A
MAGIC GLOBE 28 2 GEOMETRIC MATRIX MODELS II 39 2.1 A VECTOR SPACE AND
ITS DUAL 39 2.2 A POINT ON A GRASSMANNIAN 44 2.3 A CELL DECOMPOSITION IN
PROJECTIVE SPACE 48 2.4 TOPES, COVECTORS, COCIRCUITS, BIG FACE LATTICE
50 2.5 A ZONOTOPE, MINKOWSKI SUM OF LINE SEGMENTS 51 2.6 A PROJECTION OF
A CUBE 52 2.7 HYPERPLANES SPANNED BY POINT SETS, COCIRCUITS 53 2.8
MINIMAL DEPENDENT SETS, CIRCUITS 55 2.9 SUMMARY 67 2.10 WHAT IS THE
ORIENTED MATROID OF A MATRIX? 70 3 FROM MATRICES TO RANK 3 ORIENTED
MATROIDS 72 3.1 FROM A MATRIX TO ITS CHIROTOPE 72 3.2 THE BASIC RANK 2
CASE 74 3.3 A PLANAR POINT SET EXAMPLE 80 VLL VIII CONTENTS 3.4 UNIFORM
CHIROTOPES AND HYPERLINE SEQUENCES 83 3.5 CONVEX HULL OF A CHIROTOPE IN
RANK 3 83 3.6 REORIENTATION, RELABELING, SIGN REVERSAL 84 3.7 AXIOM
SYSTEMS, AN OVERVIEW 93 3.8 THREE SELECTED AXIOM SYSTEMS IN RANK 3 95
3.9 AXIOM EQUIVALENCE IN RANK 3 104 3.10 NON-REALIZABLE RANK 3 ORIENTED
MATROIDS 108 4 ORIENTED MATROIDS OF ARBITRARY RANK 111 4.1 SPHERE
SYSTEMS, ORIENTED PSEUDOSPHERES 112 4.2 CHIROTOPES, ORIENTATIONS OF ALL
SIMPLICES 114 4.3 CONTRACTION, DELETION, RELABELING, REORIENTATION 114
4.4 A POLYTOPE WITHOUT DIAGONALS NEED NOT BE A SIMPLEX 117 4.5 EXAMPLE
CLASSES OF ORIENTED MATROIDS 119 4.6 HYPERLINE SEQUENCES, ALGORITHMIC
ADVANTAGE 123 4.7 CIRCUITS AND COCIRCUITS 125 4.8 EXTENSIONS OF ORIENTED
MATROIDS 127 5 FROM ORIENTED MATROIDS TO FACE LATTICES 129 5.1 CONVEX
HULLS FROM CHIROTOPES 132 5.2 A NEIGHBORLY 3-SPHERE WITH TEN VERTICES
136 5.3 HEEGARD SPLITTING OF THE 3-SPHERE 138 5.4 AN INTERESTING
3-SPHERE DUE TO KLEINSCHMIDT 142 6 FROM FACE LATTICES TO ORIENTED
MATROIDS I 144 6.1 FINDING MATROID POLYTOPES DIRECTLY 145 6.2 TWO
3-SPHERES OF BRUCKNER AND ALTSHULER 145 6.3 HOW TO FIND A HEEGARD
SPLITTING OF A SPHERE 150 6.4 THE DUAL FACE LATTICE OF ALTSHULER S
3-SPHERE NO. 963 156 6.5 IS ALTSHULER S 3-SPHERE NO. 963 POLYTOPAL? 158
7 FROM FACE LATTICES TO ORIENTED MATROIDS II 164 7.1 MATROID POLYTOPES
VIA EXTENSIONS 164 7.2 RANK 5 UNIFORM MATROID POLYTOPES 165 7.3 RANK 5
NON-UNIFORM MATROID POLYTOPES 167 7.4 CONTRACTION FOR MATROID POLYTOPES
168 7.5 CHIROTOPES AND HYPERLINE SEQUENCES 170 7.6 MATROID POLYTOPE
EXTENSIONS, FUNCTION DEPENDENCIES 174 7.7 THE ESSENTIAL PART OF THE
EXTENSION ALGORITHM 175 7.8 A 3-SPHERE WITH TEN DU RER POLYHEDRA 179 7.9
ALTSHULER S SPHERE NO. 425 190 7.10 A 3-SPHERE OF GEVAY, SELF-POLAR-DUAL
EXAMPLE 193 CONTENTS IX 7.11 ON A 3-SPHERE OF MCMULLEN 196 7.12 SIMPLE
SPHERES WITH SMALL NUMBER OF FACETS 205 8 FROM ORIENTED MATROIDS TO
MATRICES 206 8.1 AN EXAMPLE OF A 5-SPHERE DUE TO SHEMER 206 8.2 LINEAR
PROGRAMMING CAN HELP 208 8.3 THE FINAL POLYNOMIAL METHOD 213 8.4
SOLVABILITY SEQUENCES 213 8.5 COMBINATORIAL ARGUMENTS 213 8.6
NON-REALIZABLE ORIENTED MATROIDS 213 8.7 FINDING A POLYTOPE WITH A GIVEN
FACE LATTICE 214 9 COMPUTATIONAL SYNTHETIC GEOMETRY 217 9.1 ON MOBIUS S
TORUS AND CSASZAR S POLYHEDRON 218 9.2 ON HEAWOOD S MAP AND SZILASSI S
POLYHEDRON 222 9.3 TWO GENERAL PROBLEMS 227 9.4 ON THE STEINITZ PROBLEM
FOR TORI 228 9.5 SPATIAL POLYHEDRA 237 9.6 NON-REALIZABLE POLYHEDRA 246
9.7 NON-REALIZABLE TRIANGULATED ORIENTABLE SURFACES 249 10 SOME ORIENTED
MATROID APPLICATIONS 259 10.1 TRIANGULATIONS OF POINT SETS 259 10.2
ORIENTED MATROID PROGRAMMING 259 10.3 LINE CONFIGURATIONS AND ALGEBRAIC
SURFACES 260 10.4 CONFIGURATIONS OF POINTS AND LINES 260 10.5 PROJECTIVE
INCIDENCE THEOREMS 266 10.6 CONCEPT ANALYSIS 271 10.7 TRIANGULAR
PSEUDOLINE ARRANGEMENTS 272 10.8 ORIENTED MATROIDS ARE GENERALIZED
PLATONIC SOLIDS 275 10.9 CURVES ON SURFACES INTERSECTING PAIRWISE ONCE
276 10.10 CURVES ON SURFACES INTERSECTING AT MOST ONCE 280 10.11 ON THE
ERD6S-SZEGERES CONJECTURE 282 11 SOME INTRINSIC ORIENTED MATROID
PROBLEMS 285 11.1 ENUMERATION OF SMALL EXAMPLE CLASSES 285 11.2 THE
MUTATION PROBLEM 286 11.3 ON THE CUBE PROBLEM OF LAS VERGNAS 292
APPENDIX A A HASKELL PRIMER 294 A. 1 ABOUT HASKELL B. CURRY 294 A.2
FIRST HASKELL FUNCTIONS AND INTRODUCTION 295 X CONTENTS APPENDIX B
SOFTWARE, HASKELL FUNCTIONS, AND EXAMPLES 299 B.I SOFTWARE ABOUT
ORIENTED MATROIDS 299 B.2 USED BASIC HASKELL FUNCTIONS 300 APPENDIX C
LIST OF SYMBOLS 313 REFERENCES 314 INDEX , 322
|
| adam_txt |
COMPUTATIONAL ORIENTED MATROIDS EQUIVALENCE CLASSES OF MATRICES WITHIN A
NATURAL FRAMEWORK JURGEN G. BOKOWSKI DARMSTADT UNIVERSITY OF TECHNOLOGY
GERMANY CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE PAGE XI 1 GEOMETRIC
MATRIX MODELS I 1 1.1 A CONVEX POLYTOPE 4 1.2 A VECTOR CONFIGURATION 10
1.3 A CHIROTOPE, ORIENTATIONS OF ALL SIMPLICES 14 1.4 A CENTRAL
HYPERPLANE CONFIGURATION 17 1.5 A GREAT-SPHERE ARRANGEMENT 18 1.6 A SET
OF HYPERLINE SEQUENCES 19 1.7 A POINT SET ON A SPHERE 25 1.8 A SIGNED
AFFINE POINT SET 25 1.9 A SET OF ORIENTED AFFINE HYPERPLANES 27 1.10 A
MAGIC GLOBE 28 2 GEOMETRIC MATRIX MODELS II 39 2.1 A VECTOR SPACE AND
ITS DUAL 39 2.2 A POINT ON A GRASSMANNIAN 44 2.3 A CELL DECOMPOSITION IN
PROJECTIVE SPACE 48 2.4 TOPES, COVECTORS, COCIRCUITS, BIG FACE LATTICE
50 2.5 A ZONOTOPE, MINKOWSKI SUM OF LINE SEGMENTS 51 2.6 A PROJECTION OF
A CUBE 52 2.7 HYPERPLANES SPANNED BY POINT SETS, COCIRCUITS 53 2.8
MINIMAL DEPENDENT SETS, CIRCUITS 55 2.9 SUMMARY 67 2.10 WHAT IS THE
ORIENTED MATROID OF A MATRIX? 70 3 FROM MATRICES TO RANK 3 ORIENTED
MATROIDS 72 3.1 FROM A MATRIX TO ITS CHIROTOPE 72 3.2 THE BASIC RANK 2
CASE 74 3.3 A PLANAR POINT SET EXAMPLE 80 VLL VIII CONTENTS 3.4 UNIFORM
CHIROTOPES AND HYPERLINE SEQUENCES 83 3.5 CONVEX HULL OF A CHIROTOPE IN
RANK 3 83 3.6 REORIENTATION, RELABELING, SIGN REVERSAL 84 3.7 AXIOM
SYSTEMS, AN OVERVIEW 93 3.8 THREE SELECTED AXIOM SYSTEMS IN RANK 3 95
3.9 AXIOM EQUIVALENCE IN RANK 3 104 3.10 NON-REALIZABLE RANK 3 ORIENTED
MATROIDS 108 4 ORIENTED MATROIDS OF ARBITRARY RANK 111 4.1 SPHERE
SYSTEMS, ORIENTED PSEUDOSPHERES 112 4.2 CHIROTOPES, ORIENTATIONS OF ALL
SIMPLICES 114 4.3 CONTRACTION, DELETION, RELABELING, REORIENTATION 114
4.4 A POLYTOPE WITHOUT DIAGONALS NEED NOT BE A SIMPLEX 117 4.5 EXAMPLE
CLASSES OF ORIENTED MATROIDS 119 4.6 HYPERLINE SEQUENCES, ALGORITHMIC
ADVANTAGE 123 4.7 CIRCUITS AND COCIRCUITS 125 4.8 EXTENSIONS OF ORIENTED
MATROIDS 127 5 FROM ORIENTED MATROIDS TO FACE LATTICES 129 5.1 CONVEX
HULLS FROM CHIROTOPES 132 5.2 A NEIGHBORLY 3-SPHERE WITH TEN VERTICES
136 5.3 HEEGARD SPLITTING OF THE 3-SPHERE 138 5.4 AN INTERESTING
3-SPHERE DUE TO KLEINSCHMIDT 142 6 FROM FACE LATTICES TO ORIENTED
MATROIDS I 144 6.1 FINDING MATROID POLYTOPES DIRECTLY 145 6.2 TWO
3-SPHERES OF BRUCKNER AND ALTSHULER 145 6.3 HOW TO FIND A HEEGARD
SPLITTING OF A SPHERE 150 6.4 THE DUAL FACE LATTICE OF ALTSHULER'S
3-SPHERE NO. 963 156 6.5 IS ALTSHULER'S 3-SPHERE NO. 963 POLYTOPAL? 158
7 FROM FACE LATTICES TO ORIENTED MATROIDS II 164 7.1 MATROID POLYTOPES
VIA EXTENSIONS 164 7.2 RANK 5 UNIFORM MATROID POLYTOPES 165 7.3 RANK 5
NON-UNIFORM MATROID POLYTOPES 167 7.4 CONTRACTION FOR MATROID POLYTOPES
168 7.5 CHIROTOPES AND HYPERLINE SEQUENCES 170 7.6 MATROID POLYTOPE
EXTENSIONS, FUNCTION DEPENDENCIES 174 7.7 THE ESSENTIAL PART OF THE
EXTENSION ALGORITHM 175 7.8 A 3-SPHERE WITH TEN DU'RER POLYHEDRA 179 7.9
ALTSHULER'S SPHERE NO. 425 190 7.10 A 3-SPHERE OF GEVAY, SELF-POLAR-DUAL
EXAMPLE 193 CONTENTS IX 7.11 ON A 3-SPHERE OF MCMULLEN 196 7.12 SIMPLE
SPHERES WITH SMALL NUMBER OF FACETS 205 8 FROM ORIENTED MATROIDS TO
MATRICES 206 8.1 AN EXAMPLE OF A 5-SPHERE DUE TO SHEMER 206 8.2 LINEAR
PROGRAMMING CAN HELP 208 8.3 THE FINAL POLYNOMIAL METHOD 213 8.4
SOLVABILITY SEQUENCES 213 8.5 COMBINATORIAL ARGUMENTS 213 8.6
NON-REALIZABLE ORIENTED MATROIDS 213 8.7 FINDING A POLYTOPE WITH A GIVEN
FACE LATTICE 214 9 COMPUTATIONAL SYNTHETIC GEOMETRY 217 9.1 ON MOBIUS'S
TORUS AND CSASZAR'S POLYHEDRON 218 9.2 ON HEAWOOD'S MAP AND SZILASSI'S
POLYHEDRON 222 9.3 TWO GENERAL PROBLEMS 227 9.4 ON THE STEINITZ PROBLEM
FOR TORI 228 9.5 SPATIAL POLYHEDRA 237 9.6 NON-REALIZABLE POLYHEDRA 246
9.7 NON-REALIZABLE TRIANGULATED ORIENTABLE SURFACES 249 10 SOME ORIENTED
MATROID APPLICATIONS 259 10.1 TRIANGULATIONS OF POINT SETS 259 10.2
ORIENTED MATROID PROGRAMMING 259 10.3 LINE CONFIGURATIONS AND ALGEBRAIC
SURFACES 260 10.4 CONFIGURATIONS OF POINTS AND LINES 260 10.5 PROJECTIVE
INCIDENCE THEOREMS 266 10.6 CONCEPT ANALYSIS 271 10.7 TRIANGULAR
PSEUDOLINE ARRANGEMENTS 272 10.8 ORIENTED MATROIDS ARE GENERALIZED
PLATONIC SOLIDS 275 10.9 CURVES ON SURFACES INTERSECTING PAIRWISE ONCE
276 10.10 CURVES ON SURFACES INTERSECTING AT MOST ONCE 280 10.11 ON THE
ERD6S-SZEGERES CONJECTURE 282 11 SOME INTRINSIC ORIENTED MATROID
PROBLEMS 285 11.1 ENUMERATION OF SMALL EXAMPLE CLASSES 285 11.2 THE
MUTATION PROBLEM 286 11.3 ON THE CUBE PROBLEM OF LAS VERGNAS 292
APPENDIX A A HASKELL PRIMER 294 A. 1 ABOUT HASKELL B. CURRY 294 A.2
FIRST HASKELL FUNCTIONS AND INTRODUCTION 295 X CONTENTS APPENDIX B
SOFTWARE, HASKELL FUNCTIONS, AND EXAMPLES 299 B.I SOFTWARE ABOUT
ORIENTED MATROIDS 299 B.2 USED BASIC HASKELL FUNCTIONS 300 APPENDIX C
LIST OF SYMBOLS 313 REFERENCES 314 INDEX , 322 |
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| id | DE-604.BV021786516 |
| illustrated | Illustrated |
| index_date | 2024-07-02T15:43:05Z |
| indexdate | 2024-07-09T20:44:04Z |
| institution | BVB |
| isbn | 9780521849302 0521849306 |
| language | English |
| lccn | 2006295891 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014999227 |
| oclc_num | 61757123 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-2070s |
| owner_facet | DE-91G DE-BY-TUM DE-2070s |
| physical | XIII, 323 S. Ill., graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Bokowski, Jürgen 1943- Verfasser (DE-588)143597590 aut Computational oriented matroids equivalence classes of matrices within a natural framework Jürgen G. Bokowski 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2006 XIII, 323 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. 314-321) and index Oriented matroids Orientiertes Matroid (DE-588)4232299-6 gnd rswk-swf Orientiertes Matroid (DE-588)4232299-6 s DE-604 http://www.loc.gov/catdir/enhancements/fy0668/2006295891-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0668/2006295891-t.html Table of contents only HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014999227&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bokowski, Jürgen 1943- Computational oriented matroids equivalence classes of matrices within a natural framework Oriented matroids Orientiertes Matroid (DE-588)4232299-6 gnd |
| subject_GND | (DE-588)4232299-6 |
| title | Computational oriented matroids equivalence classes of matrices within a natural framework |
| title_auth | Computational oriented matroids equivalence classes of matrices within a natural framework |
| title_exact_search | Computational oriented matroids equivalence classes of matrices within a natural framework |
| title_exact_search_txtP | Computational oriented matroids equivalence classes of matrices within a natural framework |
| title_full | Computational oriented matroids equivalence classes of matrices within a natural framework Jürgen G. Bokowski |
| title_fullStr | Computational oriented matroids equivalence classes of matrices within a natural framework Jürgen G. Bokowski |
| title_full_unstemmed | Computational oriented matroids equivalence classes of matrices within a natural framework Jürgen G. Bokowski |
| title_short | Computational oriented matroids |
| title_sort | computational oriented matroids equivalence classes of matrices within a natural framework |
| title_sub | equivalence classes of matrices within a natural framework |
| topic | Oriented matroids Orientiertes Matroid (DE-588)4232299-6 gnd |
| topic_facet | Oriented matroids Orientiertes Matroid |
| url | http://www.loc.gov/catdir/enhancements/fy0668/2006295891-d.html http://www.loc.gov/catdir/enhancements/fy0668/2006295891-t.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014999227&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bokowskijurgen computationalorientedmatroidsequivalenceclassesofmatriceswithinanaturalframework |