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Theory of matroids

Theory of matroids

자료유형
단행본
개인저자
White, Neil.
서명 / 저자사항
Theory of matroids / edited by Neil White.
발행사항
Cambridge [Cambridgeshire] ;   New York :   Cambridge University Press,   c1986.  
형태사항
xvii, 316 p. : Ill., Genealogical tables ; 25 cm.
총서사항
Encyclopedia of mathematics and its applications ;v. 26.
ISBN
0521309379
서지주기
Includes bibliographies and index.
일반주제명
Matroids.
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001 000000922075
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008 850318s1986 enkaj b 00100 eng
010 ▼a 85006682
020 ▼a 0521309379
040 ▼a DLC ▼c DLC ▼d 244002
049 0 ▼l 452076705 ▼l 452045482
050 0 0 ▼a QA166.6 ▼b .T44 1986
082 0 0 ▼a 511/.6 ▼2 19
090 ▼a 512.3 ▼b W586t
100 1 ▼a White, Neil.
245 1 0 ▼a Theory of matroids / ▼c edited by Neil White.
260 ▼a Cambridge [Cambridgeshire] ; ▼a New York : ▼b Cambridge University Press, ▼c c1986.
300 ▼a xvii, 316 p. : ▼b Ill., Genealogical tables ; ▼c 25 cm.
440 0 ▼a Encyclopedia of mathematics and its applications ; ▼v v. 26.
504 ▼a Includes bibliographies and index.
650 0 ▼a Matroids.

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No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
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컨텐츠정보

목차


CONTENTS
List of Contributors = ⅸ
Series Editor's Statement = xi
Foreword by Gian-Carlo Rota = xiii
Preface = xv
Chapter 1 Examples and Basic Concepts / Henry Crapo = 1
 1.1 Examples from Linear Algebra and Projective Geometry = 1
 1.2 Further Algebraic Examples = 12
 1.3 Combinatorial Examples = 16
 1.4 Structure and Related Geometries = 25
 Exercises = 27
Chapter 2 Axiom Systems / Giorgio Nicoletti ; Neil White = 29
 2.1 Basis Axioms = 30
 2.2 Other Families of Subsets = 32
 2.3 Closure and Rank = 38
 2.4 Combinatorial Geometries and Infinite Matroids = 42
 Exercises = 43
 References = 44
Chapter 3 Lattices / Ulrich Faigle = 45
 3.1 Posets and Lattices = 46
 3.2 Modularity = 49
 3.3 Semimodular Lattices of Finite Length = 51
 3.4 Geometric Lattices = 53
 3.5 Decomposition of Geometric Lattices = 56
 3.6 Projective Geometry and Modular Geometric Lattices = 58
 Exercises = 60
 References = 61
Chapter 4 Basis-Exchange Properties / Joseph P. S. Kung = 62
 4.1 Bracket Identities and Basis-Exchange Properties = 62
 4.2 The Exchange Graph = 64
 4.3 Multiple and Alternating Exchanges = 66
 Historical Notes = 69
 Exercises = 69
 References = 73
Chapter 5 Orthogonality / Henry Crapo = 76
 5.1 Introduction = 76
 5.2 Orthogonal Geometries = 77
 5.3 Vector Geometries and Function-Space Geometries = 81
 5.4 Orthogonality of Vector Geometries = 85
 5.5 Orthogonality of Simplicial Geometries = 87
 5.6 Orthogonality of Planar Graphic Geometries = 90
 5.7 Research Problem : Orthogonality between Other Pairs of Simplicial Geometries = 91
 5.8 The Orthogonal of a Structure Geometry = 94
 References = 96
Chapter 6 Graphs and Series-Parallel Networks / James Oxiey = 97
 6.1 Polygon Matroids, Bond Matroids, and Planar Graphs = 98
 6.2 Connectivity for Graphs and Matroids = 107
 6.3 Whitney's 2-Isomorphism Theorem = 110
 6.4 Series-Parallel Networks = 116
 Exercises = 120
 References = 125
Chapter 7 Constructions / Thomas Brylawski = 127
 7.1 Introduction = 127
 7.2 Isthmuses and Loops = 128
 7.3 Deletions, Submatroids, and Extensions = 130
 7.4 Contractions, Minors, and Lifts = 138
 7.5 Truncations, Lifts, and Matroid Bracing = 162
 7.6 Direct Sum and Its Generalizations = 173
 7.7 Lower Truncations = 193
 7.8 Index of Constructions = 201
 Exercises = 209
 References = 222
Chapter 8 Strong Maps / Joseph P. S. Kung = 224
 8.1 Minors and Strong Maps = 224
 8.2 The Factorization Theorem = 230
 8.3 Elementary Quotient Maps = 237
 8.4 Further Topics = 240
 Historical Notes = 242
 Exercises = 243
 References = 252
Chapter 9 Weak Maps / Joseph P. S. Kung ; Hien Q. Nguyen = 254
 9.1 The Weak Order = 254
 9.2 Weak Cuts = 256
 9.3 Rank-preserving Weak Maps = 260
 9.4 Simple Weak Maps of Binary Matroids = 262
  Historical Notes = 267
  Exercises = 268
  References = 270
Chapter 10 Semimodular Functions / Hien Q. Nguyen = 272
 10.1 General Properties of Semimodular Functions = 273
 10.2 Expansions and Dilworth's Embedding = 275
 10.3 Reductions = 282
 10.4 Applications of Expansions and Reductions = 289
 Historical Notes = 296
 References = 297
Appendix of Matroid Cryptomorphisms / Thomas Brylawski = 298
 Axiomatizations for the Matroid M(E) = 300
 Cryptomorphisms = 304
 Prototypical Examples = 305
 Special Cryptomorphisms Characterizing Binary Matroids = 310
Index = 313


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