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V. Bryant — Independence theory in combinatorics: An introductory account with applications to graphs and transversals (Chapman and Hall mathematics series)
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Название: Independence theory in combinatorics: An introductory account with applications to graphs and transversals (Chapman and Hall mathematics series)Автор: V. Bryant Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель без номеров страниц ed2k: ed2k stats Год издания: 1980Количество страниц: 149Добавлена в каталог: 24.04.2020Операции: Положить на полку |
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Affine independence 8 Affine rank 9 Affine subspace 9 Affinely independent set 8 Affinely representable 107 Algorithmic construction of heaviest bases 24 Algorithmic proof of Hall's theorem 68 Alternating path 70 75 ARC 48 Base orderability 103 Bases of a maximum weight (heaviest) 24 25 Bases of a vector space 7 Bases of an independence space 14 Bases, algorithm for heaviest 24 Bases, axioms for 16 17 Bases, equal cardinality of 14 Binary independence space 112 Bipartite complete 5 Bipartite graph 5 29 Bipartite independence structures induced by 29 32 Birkhoff, G. 2 Cardinality of a set 3 Characteristic of a field 113 Characteristic of a set 113 Circuit (in an independence space) 15 Circuit (in an independence space), space 38 Circuits, axioms for 16 17 Circuits, fundamental set of 37 Common partial transversal 95 Common transversal 86 Complete bipartite graph 5 Complete graph 4 Component of a graph 5 Connected graph 5 Connected independence space 37 Connected set of edges 62 Contraction of a graph 60 Contraction of an independence structure 20 Contractionof a vector space 37 Cutset (in a graph) 43 Cutset space 43 Cutset structure 43 Cycle (in a graph) 41 Cycle space 41 Cycle structure 41 Degree of a vertex 3 dependence axioms of 2 36 Dependence, axioms for 2 36 Dependence, relation of 2 Dependent set 13 Dimension of a vector space 7 Direct sum of independence structures 21 Directed graph 80 Disconnecting set of edges 43 Disjoint paths 80 Distinct representatives 66 Dual indepedence structures 22 Dual indepedence structures, rank of 22 Dual of transversal structure 79 83 Dual structures in a graph 45 Dual, geometric (of planar graph) 47 Edge (in a graph), 3 Edge directed 80 Edge endpoints of 3 Edge-set (through a vertex) 53 Endpoint of a path 5 Endpoint of an edge 3 Erection 39 Euler's formula 56 Face of a planar representation 47 Family of elements 3 Family of sets 3 Fano geometry 102 Finite-dimensional vector space 6 7 Finiteness assumption 2 Flat (in an independence space) 19 Flat as intersection of hyperplanes 37 Flat spanned by a set 19 Forests (in a graph) 5 Forests partitioning into 58 Fundamental set of circuits 37 Gammoid 82 Gammoid strict 82 Geometric dual of planar graph 47 Graph 3 Graph bipartite 5 Graph complete 4 Graph complete bipartite 5 Graph connected 5 Graph directed 80 Graph planar 46 Graphic spaces 45 Graphoid 40 Greedy algorithm 24 Hall's theorem 68 Hall, P. 2 66 Hamiltonian path 95 Heaviest bases 24 Hereditary property of independent sets 13 Hyperplane 37 Incidence matrix of a graph 55 Incidence of a family of sets 130 Independence linear 6 Independence on a graph 41 43 Independence space 13 Independence structure 13 Independence, affine 8 Independence, associated with a family of sets 75 Independent sets, axioms for 13 Independent sets, transversal 67 Induced structures 20 29 Initial vertex 80 Isomorphism of independence structures 49 Join of vertices by a path 5 Join of vertices by an edge 3 Latin rectangle 89 Latin square 89 Linear independence 6 Linear rank (or dimension) 7 Linear representability 104 Linear representability of graphic spaces 105 Linear representability of induced spaces 108 Linear representability of transversal spaces 105 Linearly dependent set 6 Linearly independent set 6 Linkage theorem 84 Linked sets 81 MacLane S. 2 Mapping, rank preserving 104 Matching (in a graph) 5 30 Matching structure 99 Matroid 1 2 Menger's Theorem 89 97 Menger, K. 88 Minimal presentation of a transversal structure 96 Minor of an independence space 102 Partial transversal 65 Path in a directed graph 80 Path in a graph 5 Path initial and terminal vertices of 80 Path, Hamiltonian 95 Permutation product 78 Planar geometric dual of 47 Planar graph 46 Planar representation 46 Planar representation, face of 47 Power set 3 Pre-geometry 1 Presentation minimal 96 Presentation of transversal structure 96 Product of independence structures 40 Product of vectors 9 Proper truncation 26 Quotient space 37 Rado's theorem 74 Rado, R. 2 Rank 15 Rank axioms for 16 26 Rank function 15 Rank-preserving mapping 104 Regular independence space 112 Replacement property of independent sets 13 Replacement theorems (an a vector space) 6 8 Representability affine 107 Representability linear 104 Representability of an independence space 101 Representability of induced structures 108 Representatives distinct 66 94 Representatives of a family of sets 94 Restriction of an independence structure 14 Separation (in a directed graph) 88 span 19 Spanning set 37 Spanning tree 42 Star (in a directed graph) 81 Strict gammoid 82 Subfamily 3 87 Submodular function 28 Submodular inequality 15 Submodular structures induced by 26 Sum direct 21 Sum of independence structures 33 Symmetric difference 2 System distinct 66 94 System of representatives 94 Terminal vertex 80 Translate of a set of vectors 8 Transversal common 86 Transversal dual of 79 83 Transversal independent 67 Transversal of a family of sets 65 Transversal partial 65 Transversal space 75 Transversal structure 75 TREE 5 Tree spanning 42 Truncation of an independence structure 26 Truncation proper 26 Tutte, W.T. 2 102 Tutte, W.T., characterization theorems of 2 102 Undirected strict gammoid 97 Universal structure 14 Vamos space 114 Van der Waerden, B.L. 2 Vector spaces associated with graphic spaces 50 54 Vector spaces associated with transversal spaces 75 77 Vector spaces, affine independence in 8 Vector spaces, linear independence in 6 Vertex (in a graph) 3 Vertex degree of 3 Weight 24 57 Wheel 62 Whitney, H. 2
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