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Combinatorial matrix classes:

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Bibliographische Detailangaben
Beteilige Person:	Brualdi, Richard A. 1939- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Cambridge [u.a.] Cambridge Univ. Press 2006
Ausgabe:	1. publ.
Schriftenreihe:	Encyclopedia of mathematics and its applications 108
Schlagwörter:	Kombinatorik - Matrizentheorie Matrix <Mathematik> - Kombinatorische Analysis Combinatorial analysis Matrices Kombinatorische Analysis Matrizentheorie Matrix > Mathematik Kombinatorik Algebra
Links:	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
Umfang:	X, 544 S.
ISBN:	0521865654 9780521865654

Internformat

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Datensatz im Suchindex

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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
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author	Brualdi, Richard A. 1939-
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isbn	0521865654 9780521865654
language	English
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publisher	Cambridge Univ. Press
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series	Encyclopedia of mathematics and its applications
series2	Encyclopedia of mathematics and its applications
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_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

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