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Rota G.-C. — Studies in combinatorics (MAA Studies in Mathematics, volume 17)
Rota G.-C. — Studies in combinatorics (MAA Studies in Mathematics, volume 17)

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Название: Studies in combinatorics (MAA Studies in Mathematics, volume 17)

Автор: Rota G.-C.

Аннотация:

Combinatorics has recently awakened from a long slumber, which began at the time of Euler. It has emerged as a new subject standing at the crossroads between pure and applied mathematics, the center of bustling activity, a simmering pot of new problems and exciting speculations.
The seven papers of this survey represent a wide enough sampling of current trends, from which the reader may, at least, extrapolate some of the missing material. They bear in common the one characteristic of contemporary combinatorics: striving for general new results, while using old and new problems as a test of efficiency.
The introduction to matroid theory by Brylawski and Kelly describes a theory whose background — at least from a distance — is the four-color conjecture, much like the background of algebraic number theory was, at least at the beginning, Fermat's conjecture. It matters little that neither theory has succeeded in solving its motivating problem...


Язык: en

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1978

Количество страниц: 274

Добавлена в каталог: 04.12.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$k$-binomial expansion      62
$k$-coloring, proper      213
$k$-family      28
$k$-flow, proper      214
$n$-set      3
$P$ -partition      116
$P$ -partition, order-reversing      116
$P$ -partition, strict      116
$P$ -partition, surjective      117
$P$ -partition, surjective strict      117
$r$ -partition of a set      130
$r$ -partition of a set, blocks of      130
$r$ -partition of a set, convolutional formula for      132
$r$ -partition of a set, type of      131
$t$ -independent subset      212
Alder, H. L.      140
Algebraic function      123
Algebraic function, irreducible      123
Alltop, W. O.      251
Alter, R.      140
Amitsur, S. A.      7 19
Anand, H.      139 140
Anderson, I.      76
Andrews, G. E.      140 141
Antichain      23
Antichain, compression of      66
Antichain, order-ideal of      66
Assmus, E. F.      251
Axiom of Choice      146
Baire category theorem      82
Baker, K.      36 77
Balanced incomplete block design      220
Basterfield, J. G.      215
Baumert, L. D.      238 251
Baumgartner, J. E.      98
Bell number      130
Bender, E. A.      105 116 138 140
Berge, C.      217
Berlekamp, E.      98 168 178
Bipartite graph      81
Bipartite graph, $r$ - Ramsey      81
Bipartite graph, $r$-coloring      81
Bipartite graph, monochromatic vertex      81
Biplane      12
Birkhoff, G.      190 215
Bixby, R.      199 215
Block of incidence structure      219
Block of partition      130
BoIIobas, B.      46 47 77
Bose, R. C.      219 240 245 247 251 252
Bracket ring      203
Bridges, W. G.      14 19 20 21
Brown, T.      198
Brown, W. G.      77 140
Brualdi, R. A.      20 203 215
Bruck, R. H.      10 233 251
Brylawski, T.      200 215 217
Burr, S.      93 98
Cameron, P. J.      20
Canonical form      68 69
Cascade      63
Cates, M.      93 98
Chain      23
Chain, maximal      35
Characteristic set      201
Chernoff, H.      178
Chowla, S.      10 252
Chromatic number      157
Chvat$\acute{a}$l, V.      98
Clements, G.      64 65 69 73
CLIQUE      144
Coding problem      211
Coloring, balanced      32
Combinatorial geometry      182
Combinatorial pregeometry      180
Compression      64 69
Compression,$i$      73
Compression,reverse      68
Comtet, L.      123 129 140
Construction, direct      142 230
Construction, recursive      142 244
Counting function      101
Crapo, H. H.      24 77 188 215 216
Crawley, P.      216
critical exponent      210
Critical problem      210
Daykin, D. E.      58 65 67 76 77
Deb runner, H.      216
DeBruijn, N. G.      20 30 34 76 77
Dedekind, R.      33
Dembowski, P.      12 20 220 252
Desargues configuration      200
Design      220 221
Design, ($\nu$, $k$, $\lambda$)      8
Design, Abelian      232
Design, Abelian, multiplier      233
Design, group divisible      226
Design, Hadamard      12
Design, lambda      13
Design, partially balanced      222
Design, resolvable      2261
Design, symmetric      222 228
Design, transversal      224
Design, type I lambda      13
Deuber, W.      85 92 98
Diagonal product      5
Difference set      231 238
Difference set, Type $B_{0}$      239
Difference set, Type $GMW$      239
Difference set, Type $H_{6}$      239
Difference set, Type $O$      239
Difference set, Type $O_{0}$      239
Difference set, Type $Q$      239
Difference set, Type $S$      238
Difference set, Type $T$      239
Difference set, Type $W_{4}$      239
Difference set, Type B      239
Dilworth, R. P.      4 20 28 29 34 77 205 216
Doubilet, P.      105 140
Dowling, T. A.      216
Duffin, R. J.      200 216
Dumir, V. C.      139 140
Dushnik, B.      83 98
Dwass, M.      178
Edelberg, M.      27 78
Edmonds, J.      18 20 188 216
Egerv$\acute{a}$ry      4
Ehrhart, E.      140
entropy      170
Enumeration      100
Enumeration, fundamental problem of      101
Erd$\acute{e}$lyi, A.      129 140
Erd$\ddot{o}$s, P.      20 22 28 29 34 40 44 45 50 55 67 68 71 73 74 75 77 83 98 143 145 153 158 160 162 178 252
Error vector      172
Etherington, I. M.H.      129 140
Euler conjecture      219
Euler, L.      116 219 245
Eulerian number      120
Family of sets, $f$-sequence      64
Family of sets, compressed      64
Fisher, R. A.      221 252
Foata, D.      140
Folkman, J.H.      85 98
Ford, L. R., Jr      4 20 79
Freese, R.      28 77
Frobenius      4
Fulkerson, D. R.      4 20 79 188 216
Gallai      94 201
Gaussian coefficients      26 207
General position      181
Generating function(s)      100
Generating function(s), chromatic      103
Generating function(s), Dirichlet      104
Generating function(s), doubly exponential      103
Generating function(s), exponential      102
Generating function(s), Hadamard product of      114
Generating function(s), in infinitely many variables      104
Generating function(s), ordinary      102
Generating function(s), two-variable      103
Geometry, (see combinatorial geometry) geometry, simplicial      189
Gessel, I.      141
girth      158
Gleason, A. M.      97 99
Godfrey, J.      65
Goethals, J. M.      20
Goldman, J. R.      77 105 140
Goodman, A. W.      20
Gordon, B.      116 239 252
Gould, H. W.      140
Graeco — Latin square      245
Graham, R. L.      37 77 98 99 144 151 178
Graph, bipartitie (see bipartite graph) graph, Hamiltonian      166 193
Graph, Kuratowski      199
Graph, planar      167
Graph, polygon matroid of      185
Graph, random      146
Graph, regular      242
Graph, strongly regular      242
Grassmannian      204
Graver, J. E.      99 216
Greene, C.      29 30 34 46 77 78 216 217
Greenwood, R. E.      97 99
Group code      177
Grunbaum, B.      216
Gupta, H.      139 140
Hadwiger, H.      216
Hajnal, A.      98
Hall, M., Jr      8 12 20 140 233 248 252
Hall, P.      4 20 39 78
Hamming code      174
Hamming metric      171 211
Hanani, H.      246 248 251 252
Hansel, G.      33 79
Hardy, G. H.      116 140
Harper, L. H.      37 40 77 78 79
Harris, B.      140
Hautus, M. L.J.      141
Henle, M.      105 140
Herzog, M.      77
Higman, D. E.      252
Hilton, A. J. W.      65 77
Hindman, N.      92 93 98 99
Hoffman, A. J.      16 20
Hsieh, W. N.      40 47 48 74 78
Incidence algebra      106
Incidence algebra, reduced      106
Incidence structure(s)      219
Incidence structure(s), automorphism      231
Incidence structure(s), isomorphic      231
Independent set, affinely      181
Independent set, of points in a matroid      180
Independent set, of vertices in a graph      144
Ingleton, A.      216
jacobi      116
Jaeger, F.      214 217
Jurkat, W.B.      6 20
K$\ddot{o}$nig, D.      4 5 18
Katona, G. O. H.      22 32 40 44 46 47 61 64 66 67 69 70 74 75 78
Kelly, D. G.      215 216
Kelly, J. B.      20 178
Kelly, L. B.      178
Kelly, L. M.      215
Kennedy, D.      216
Kirkman, Rev. T. P.      218 252
Klarner, D. A.      111 113 140 141
Klee, V.      216
Kleitman, D. J.      22 27 29 30 32 33 34 37 38 40 46 47 48 50 54 57 60 67 74 75 77 78 79
Knuth, D. E.      20 116 120 141
Ko, C.      44 45 50 55 67 68 71 77
Kramer, E. S.      20 25
Kreweras      116
Kronecker product of matrices      229
Kruskal, J.      61 63 64 66 67 69 70 73 74 78
Kruyswijk, D. R.      30 34 76 77
Kwiatkowsky, D.      76
Lagrange      126
Lagrange inversion formula      126
Lane, R.      252
Laplace expansion      202
Latin square      223
Lattice, geometric      185
Lattice, of multisets      25
Lattice, of partitions      27 204
Lattice, of subsets (Boolean algebra)      24 105 180
Lattice, of subspaces      26 105
Lattice, point      184
Leeb, K.      30 84 88 98 99
Levine, E.      79
Levitzki, J.      7 19
Lieb, E. H.      207 216
Lindstr$\ddot{o}$m, B.      64 69 73 77 201
Line sum      6
Lines (of incidence structure)      219
Littlewood, J. E.      74 79 116
Lov$\acute{a}$asz, L.      58 77 148 161 178
Lubell, D.      27 35 78 79
Lucas, T.D.      215 217
LYM inequality      35
LYM property      36
M$\ddot{o}$bius function      205
Mac Lane — Steinitz exchange axiom      185
Mac Lane, S.      190 216
Macauley, F. S.      70 79
MacMahon, P. A.      116 120 141
MacNeish, H. F.      247 252
MacWilliams, F. J.      20 213 252
Magic square      138
Magic square, $k$-component of      138
Magic square, $k$-component of, irreducible      138
Magic square, symmetric      139
Magnanti, T. L.      217
Main, R.      216
Mann, H. B.      221 252
Marcus, M.      8 20
Markowski, G.      79
Matrix, (0,1)      2
Matrix, doubly stochastic      7
Matrix, formal incidence      18
Matrix, fully indecomposable      19
Matrix, Hadamard      11 227
Matrix, incidence      3
Matrix, Kronecker product      229
Matrix, line of      5
Matrix, normalized Hadamard      12
Matrix, term rank of      18
Matroid      180
Matroid, affine      181
Matroid, algebraic dependence      190
Matroid, binary      199
Matroid, Boolean algebra      180
Matroid, circuits of      185
Matroid, closed sets      183
Matroid, closure      183 261
Matroid, connected      192
Matroid, contraction      193
Matroid, covering relation for      183
Matroid, cube      198
Matroid, deletion      193
Matroid, dependence      181
Matroid, dependent sets      180
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