Combinatorial matrix classes:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2006
|
| Edition: | 1. publ. |
| Series: | Encyclopedia of mathematics and its applications
108 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 544 S. |
| ISBN: | 0521865654 9780521865654 |
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Record in the Search Index
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| adam_text | ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS COMBINATORIAL MATRIX
CLASSES RICHARD A. BRUALDI UNIVERSITY OF WISCONSIN, MADISON CAMBRIDGE
UNIVERSITY PRESS CONTENTS PREFACE PAGE IX 1 INTRODUCTION 1 1.1
FUNDAMENTAL CONCEPTS 1 1.2 COMBINATORIAL PARAMETERS 5 1.3 SQUARE
MATRICES 8 1.4 AN EXISTENCE THEOREM 12 1.5 AN EXISTENCE THEOREM FOR
SYMMETRIC MATRICES 14 1.6 MAJORIZATION 15 1.7 DOUBLY STOCHASTIC MATRICES
AND MAJORIZATION 19 REFERENCES 23 2 BASIC EXISTENCE THEOREMS FOR
MATRICES WITH PRESCRIBED PROPERTIES 25 2.1 THE GALE-RYSER AND
FORD-FULKERSON THEOREMS 25 2.2 TOURNAMENT MATRICES AND LANDAU S THEOREM
32 2.3 SYMMETRIC MATRICES 39 REFERENCES 42 3 THE CLASS A(R, S) OF
(O,L)-MATRICES 45 3.1 A SPECIAL MATRIX IN A(R, S) 45 3.2 INTERCHANGES 50
3.3 THE STRUCTURE MATRIX T(R, S) 57 3.4 INVARIANT SETS * 62 3.5 TERM
RANK 69 3.6 WIDTHS AND MULTIPLICITIES . 79 3.7 TRACE 86 . 3.8 CHROMATIC
NUMBER 91 3.9 DISCREPANCY 97 3.10 RANK 100 3.11 PERMANENT 115 3.12
DETERMINANT 121 REFERENCES 129 VI CONTENTS 4 MORE ON THE CLASS A(R, S)
OF (O,L)-MATRICES 4.1 CARDINALITY OF A(R, S) AND THE RSK CORRESPONDENCE
4.2 IRREDUCIBLE MATRICES IN A(R, S) 4.3 FULLY INDECOMPOSABLE MATRICES IN
A(R, S) 4.4 A{R, S) AND Z+ (R, S) WITH RESTRICTED POSITIONS 4.5 THE
BRUHAT ORDER ON A(R, S) 4.6 THE INTEGRAL LATTICE C(R, S) 4.7 APPENDIX
REFERENCES 5 THE CLASS T(R) OF TOURNAMENT MATRICES 5.1 ALGORITHM FOR A
MATRIX IN T{R) 5.2 BASIC PROPERTIES OF TOURNAMENT MATRICES 5.3 LANDAU S
INEQUALITIES 5.4 A SPECIAL MATRIX IN T(R) 5.5 INTERCHANGES 5.6 UPSETS IN
TOURNAMENTS 5.7 EXTREME VALUES OF V(R) AND V(R) 5.8 CARDINALITY OF T(R)
5.9 THE CLASS T(R; 2) OF 2-TOURNAMENT MATRICES 5.10 THE CLASS A(R, *)O
OF (0,1)-MATRICES REFERENCES 6 INTERCHANGE GRAPHS 6.1 DIAMETER OF
INTERCHANGE GRAPHS G(R,S) 6.2 CONNECTIVITY OF INTERCHANGE GRAPHS 6.3
OTHER PROPERTIES OF INTERCHANGE GRAPHS 6.4 THE A-INTERCHANGE GRAPH G A
(R) 6.5 RANDOM GENERATION OF MATRICES IN A(R,S) AND T(R) REFERENCES 7
CLASSES OF SYMMETRIC INTEGRAL MATRICES 7.1 SYMMETRIC INTERCHANGES 7.2
ALGORITHMS FOR SYMMETRIC MATRICES 7.3 THE CLASS A(R) Q 7.4 THE CLASS
A(R) REFERENCES 8 CONVEX POLYTOPES OF MATRICES 8.1 TRANSPORTATION
POLYTOPES 8.2 SYMMETRIC TRANSPORTATION POLYTOPES 8.3 TERM RANK AND
PERMANENT 8.4 FACES OF TRANSPORTATION POLYTOPES REFERENCES CONTENTS VII
9 DOUBLY STOCHASTIC MATRICES 379 9.1 RANDOM FUNCTIONS 379 9.2 BASIC
PROPERTIES 380 9.3 FACES OF THE ASSIGNMENT POLY TOPE 385 9.4 GRAPH OF
THE ASSIGNMENT POLYTOPE 403 9.5 MAJORIZATION POLYTOPES * 417 9.6 A
SPECIAL SUBPOLYTOPE OF FT N 426 9.7 THE EVEN SUBPOLYTOPE OF Q N 433 9.8
DOUBLY SUBSTOCHASTIC AND SUPERSTOCHASTIC MATRICES 448 9.9 SYMMETRIC
ASSIGNMENT POLYTOPE 453 9.10 DOUBLY STOCHASTIC AUTOMORPHISMS 457 9.11
DIAGONAL EQUIVALENCE . 464 9.12 APPLICATIONS OF DOUBLY STOCHASTIC
MATRICES 471 9.13 PERMANENT OF DOUBLY STOCHASTIC MATRICES 482 9.14
ADDITIONAL RELATED RESULTS 495 REFERENCES 500 MASTER BIBLIOGRAPHY 511
INDEX 536
|
| adam_txt |
ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS COMBINATORIAL MATRIX
CLASSES RICHARD A. BRUALDI UNIVERSITY OF WISCONSIN, MADISON CAMBRIDGE
UNIVERSITY PRESS CONTENTS PREFACE PAGE IX 1 INTRODUCTION 1 1.1
FUNDAMENTAL CONCEPTS 1 1.2 COMBINATORIAL PARAMETERS 5 1.3 SQUARE
MATRICES 8 1.4 AN EXISTENCE THEOREM 12 1.5 AN EXISTENCE THEOREM FOR
SYMMETRIC MATRICES 14 1.6 MAJORIZATION 15 1.7 DOUBLY STOCHASTIC MATRICES
AND MAJORIZATION 19 REFERENCES 23 2 BASIC EXISTENCE THEOREMS FOR
MATRICES WITH PRESCRIBED PROPERTIES 25 2.1 THE GALE-RYSER AND
FORD-FULKERSON THEOREMS 25 2.2 TOURNAMENT MATRICES AND LANDAU'S THEOREM
32 2.3 SYMMETRIC MATRICES 39 REFERENCES 42 3 THE CLASS A(R, S) OF
(O,L)-MATRICES 45 3.1 A SPECIAL MATRIX IN A(R, S) 45 3.2 INTERCHANGES 50
3.3 THE STRUCTURE MATRIX T(R, S) 57 3.4 INVARIANT SETS '* 62 3.5 TERM
RANK 69 3.6 WIDTHS AND MULTIPLICITIES . 79 3.7 TRACE 86 . 3.8 CHROMATIC
NUMBER 91 3.9 DISCREPANCY 97 3.10 RANK 100 3.11 PERMANENT 115 3.12
DETERMINANT 121 REFERENCES 129 VI CONTENTS 4 MORE ON THE CLASS A(R, S)
OF (O,L)-MATRICES 4.1 CARDINALITY OF A(R, S) AND THE RSK CORRESPONDENCE
4.2 IRREDUCIBLE MATRICES IN A(R, S) 4.3 FULLY INDECOMPOSABLE MATRICES IN
A(R, S) 4.4 A{R, S) AND Z+ (R, S) WITH RESTRICTED POSITIONS 4.5 THE
BRUHAT ORDER ON A(R, S) 4.6 THE INTEGRAL LATTICE C(R, S) 4.7 APPENDIX
REFERENCES 5 THE CLASS T(R) OF TOURNAMENT MATRICES 5.1 ALGORITHM FOR A
MATRIX IN T{R) 5.2 BASIC PROPERTIES OF TOURNAMENT MATRICES 5.3 LANDAU'S
INEQUALITIES 5.4 A SPECIAL MATRIX IN T(R) 5.5 INTERCHANGES 5.6 UPSETS IN
TOURNAMENTS 5.7 EXTREME VALUES OF V(R) AND V(R) 5.8 CARDINALITY OF T(R)
5.9 THE CLASS T(R; 2) OF 2-TOURNAMENT MATRICES 5.10 THE CLASS A(R, *)O
OF (0,1)-MATRICES REFERENCES 6 INTERCHANGE GRAPHS 6.1 DIAMETER OF
INTERCHANGE GRAPHS G(R,S) 6.2 CONNECTIVITY OF INTERCHANGE GRAPHS 6.3
OTHER PROPERTIES OF INTERCHANGE GRAPHS 6.4 THE A-INTERCHANGE GRAPH G A
(R) 6.5 RANDOM GENERATION OF MATRICES IN A(R,S) AND T(R) REFERENCES 7
CLASSES OF SYMMETRIC INTEGRAL MATRICES 7.1 SYMMETRIC INTERCHANGES 7.2
ALGORITHMS FOR SYMMETRIC MATRICES 7.3 THE CLASS A(R) Q 7.4 THE CLASS
A(R) REFERENCES 8 CONVEX POLYTOPES OF MATRICES 8.1 TRANSPORTATION
POLYTOPES 8.2 SYMMETRIC TRANSPORTATION POLYTOPES 8.3 TERM RANK AND
PERMANENT 8.4 FACES OF TRANSPORTATION POLYTOPES REFERENCES CONTENTS VII
9 DOUBLY STOCHASTIC MATRICES 379 9.1 RANDOM FUNCTIONS 379 9.2 BASIC
PROPERTIES 380 9.3 FACES OF THE ASSIGNMENT POLY TOPE 385 9.4 GRAPH OF
THE ASSIGNMENT POLYTOPE 403 9.5 MAJORIZATION POLYTOPES * 417 9.6 A
SPECIAL SUBPOLYTOPE OF FT N 426 9.7 THE EVEN SUBPOLYTOPE OF Q N 433 9.8
DOUBLY SUBSTOCHASTIC AND SUPERSTOCHASTIC MATRICES 448 9.9 SYMMETRIC
ASSIGNMENT POLYTOPE 453 9.10 DOUBLY STOCHASTIC AUTOMORPHISMS 457 9.11
DIAGONAL EQUIVALENCE . 464 9.12 APPLICATIONS OF DOUBLY STOCHASTIC
MATRICES 471 9.13 PERMANENT OF DOUBLY STOCHASTIC MATRICES 482 9.14
ADDITIONAL RELATED RESULTS 495 REFERENCES 500 MASTER BIBLIOGRAPHY 511
INDEX 536 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T15:03:32Z |
| indexdate | 2024-07-09T20:40:51Z |
| institution | BVB |
| isbn | 0521865654 9780521865654 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014867464 |
| oclc_num | 255275372 |
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| owner_facet | DE-20 DE-91G DE-BY-TUM |
| physical | X, 544 S. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Brualdi, Richard A. 1939- Verfasser (DE-588)113645112 aut Combinatorial matrix classes Richard A. Brualdi 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2006 X, 544 S. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 108 Kombinatorik - Matrizentheorie Matrix <Mathematik> - Kombinatorische Analysis Combinatorial analysis Matrices Kombinatorische Analysis (DE-588)4164746-4 gnd rswk-swf Matrizentheorie (DE-588)4128970-5 gnd rswk-swf Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Kombinatorik (DE-588)4031824-2 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Kombinatorische Analysis (DE-588)4164746-4 s Matrix Mathematik (DE-588)4037968-1 s DE-604 Algebra (DE-588)4001156-2 s Matrizentheorie (DE-588)4128970-5 s Kombinatorik (DE-588)4031824-2 s Encyclopedia of mathematics and its applications 108 (DE-604)BV000903719 108 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014867464&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brualdi, Richard A. 1939- Combinatorial matrix classes Encyclopedia of mathematics and its applications Kombinatorik - Matrizentheorie Matrix <Mathematik> - Kombinatorische Analysis Combinatorial analysis Matrices Kombinatorische Analysis (DE-588)4164746-4 gnd Matrizentheorie (DE-588)4128970-5 gnd Matrix Mathematik (DE-588)4037968-1 gnd Kombinatorik (DE-588)4031824-2 gnd Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4164746-4 (DE-588)4128970-5 (DE-588)4037968-1 (DE-588)4031824-2 (DE-588)4001156-2 |
| title | Combinatorial matrix classes |
| title_auth | Combinatorial matrix classes |
| title_exact_search | Combinatorial matrix classes |
| title_exact_search_txtP | Combinatorial matrix classes |
| title_full | Combinatorial matrix classes Richard A. Brualdi |
| title_fullStr | Combinatorial matrix classes Richard A. Brualdi |
| title_full_unstemmed | Combinatorial matrix classes Richard A. Brualdi |
| title_short | Combinatorial matrix classes |
| title_sort | combinatorial matrix classes |
| topic | Kombinatorik - Matrizentheorie Matrix <Mathematik> - Kombinatorische Analysis Combinatorial analysis Matrices Kombinatorische Analysis (DE-588)4164746-4 gnd Matrizentheorie (DE-588)4128970-5 gnd Matrix Mathematik (DE-588)4037968-1 gnd Kombinatorik (DE-588)4031824-2 gnd Algebra (DE-588)4001156-2 gnd |
| topic_facet | Kombinatorik - Matrizentheorie Matrix <Mathematik> - Kombinatorische Analysis Combinatorial analysis Matrices Kombinatorische Analysis Matrizentheorie Matrix Mathematik Kombinatorik Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014867464&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000903719 |
| work_keys_str_mv | AT brualdiricharda combinatorialmatrixclasses |