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Andrews G.E. — The Theory of Partitions
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Название: The Theory of Partitions
Автор: Andrews G.E.
Аннотация: This book develops the theory of partitions. Simply put, the partitions of a number are the ways of writing that number as sums of positive integers. For example, the five partitions of 4 are 4, 3+1, 2+2, 2+1+1, and 1+1+1+1. Surprisingly, such a simple matter requires some deep mathematics for its study. This book considers the many theoretical aspects of this subject, which have in turn recently found applications to statistical mechanics, computer science and other branches of mathematics.With minimal prerequisites, this book is suitable for students as well as researchers in combinatorics, analysis, and number theory.
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Рубрика: Математика /
Статус предметного указателя: Готов указатель с номерами страниц
ed2k: ed2k stats
Год издания: 1976
Количество страниц: 255
Добавлена в каталог: 06.12.2005
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Предметный указатель
-function 70—71
(k, i)-negative oscillation 143—145 152—154
(k, i)-positive oscillation 143—145 152—154
Abel's lemma 209
Alder polynomials 118—119
Alder,H.L. 118
Algebraic geometry 199—200
Andrews, G.E. 14 15 31 32 52 85 86 118 119 137 138 158 177 178 200 210 211 228 243 244
Arkin, J. 85 86
Askey, R. 51 52
Atkin, A.O.L. 139 143 158 160 161 175 177 178 200
Auluck, F.C. 100 101 228
Ayoub, R. xiii 85 86
Bachman P. xiii
Bailey, W.N. 20 30 31 32
Barton, D.E. 243 244
Basic hypergeometric series 17 202 227
Basic hypergeometric series, Heine's fundamental transformation 19
Basic hypergeometric series, well-poised 106
Bateman, P.T. 101
Bell numbers 214 2]6
Bell polynomials 204—206 210 216
Bell, E.T. 204 205 206 210 211 214
Bender, E. 3 15 200 227 228
Berndt, B. 71 85 86
Binary partitions see Partition
Binary representation 116
Binomial series 54 177 see
Bipartite number 207
BLOCKS 215—217 219—220 222—223
Bohr, N. 227 228
Bratley, P. 200
Brigham, N.A. 100 101
Brylawski, T. 227 228
Bumping 185 187
Burnell, D. 243 244
Canonical basis 213—214
Carlitz, L. 31 32 52 65 66 179 183 200 202 207 210 211 228
Cauchy's integral theorem 72 93
Cauchy, A. 17 21 30 32 51 52
Cayley, A. 65 66 85 86 209
Chaundy. T.W. 200
Cheema's theorem 203
Cheema, M.S. 119 203 210 211 243 244
Chowla, S. 160
Chrystal, G. xiii
Chu — Vandermonde summation 51 61 64 227 see
Churchhouse conjecture 160 165 177
Churchhouse, R.F. 160 165 177 178 243 244
Circle method 85
class 187—188
Combinatorics 199 212ff
composition 54—58 63 65
Composition, algorithms 244
Composition, asymptotic formulas 65 68
Composition, graphical representation 55
Composition, multipartite number 54 57 179 202
Composition, vector 54 57 65
Comtet, L. xiii 14 15 210 211
Continued fraction see Ramanujan's coninued fraction
Daum, J.A. 30 32
David, F.N. 243 244
Daykin, D.E. 138
Dedekind sum 72
Dedekind's -function see -function
Derivative, composite function 204
Dickson, L.E. 227 228 243 244
Differential equations 132
Dillon, J.F. 65 66
Distributions 61—62
Dots 7
Doubilet, P. 212 227 228
Dragonette, L. 82 85 86
Durfee square 23 27—28
Durfee square, side of 28
Dyson, F.J. 142 158 161 175 178
Elliptic modular function see Modular function
Elliptic theta functions see Theta funcions
EQUIVALENCE see Partition
Erdos, P. 56 65 66 101
Erlangen, University of 137
Euler pair 138
Euler's partition theorem 24 26 122—123 139 203
Euler's pentagonal number theorem see Pentagonal number theorem
Euler, L. xiii 5 14 15 19 21 24 26 29 30 31 32 123 139 203
Eulerian series see Basic hypergeometric series
F arey fractions 72
Faa di Bruno's formula 205 210
Factorizations, unordered 210
Fall 43
Farey dissection 72 94
Ferrers graph see Partition
Fibonacci numbers 63 137
Fine, N.J. 26 29 31 32 210 211
Foata, D. 45 51 52 65 66 67
Ford circles 85
Formal power series 3
FORTRAN IV 230
Foulkes, H.O. 67
Fractional part 83
Franklin, F. 9 15 52
Fray, R.D. 67
Fruchl, R. 227 228
Fulton, J.D. 227 228
Fundamental partition ideal problem 123
Gamma function, Euler's integral 83
Gauss, C.F. 23 31 32 35 51 52
Gaussian multinomial coefficient 39
Gaussian polynomial 33 35—39 49 146 180 212 214 240
Gaussian sum 37
Generating function 221 see
Generating function, algorithms from 233
Generating function, Bell polynomials 205
Generating function, determinants 179
Generating function, finite product 42
Generating function, infinite product 3 88 203—204 209
Generating function, multipartite partitions 203
Generating function, nonmodular 85
Generating function, plane partition 185 199 210
Generating function, recurrences 179—180
Generating function, two-variable 16 128
Geometric series, finite 4
Geometric series, infinite 4
Glaisher, J.W.L. 6 9 15
Goellnitz — Gordon identities 113—114 123
Goellnitz — Gordon identities, generalization 113—114 123
Goellnitz's theorem 117—118
Goldman, J. 227 229
Gollnitz, H. 105 113 114 118 119 121 123
Gordon's multipartite partition theorem 210—211
Gordon's theorem see Rogers — Ramanujan identities
Gordon, B. 105 109 113 114 118 119 121 123 200 210 211
Greater index 42
Greatest integer function 83 157
Grosswald xiii 85 86
Group 198
Group theory 211 227
Group theory, statistical aspects 101
Group, cyclic 198
Gupta, H. 56 65 67 118 120 160 165 177 178 243 244
Gwyther, A.E. 243 244
Hagis, P. 81 82 85 86
Hahn, W. 31 32
Hankel's loop integral 75 79
Hardy, G.H. xiii 14 15 30 32 68 69 72 85 86 94 101 103 105 118 120 159 160 177
Haselgrove,C.B. 100 101
Hecke operator 160—161 167
Heine, E. 19 20 30 32 51 52
Hermite, C. 52
Hickerson, D.R. 15
Hindenburg algorithm 232 243
Hodge, W.V.D. 200
Hodges, J.H. 227 228
Homogeneous polynomial 204
Houten, L. 200 243 244
Hua, L.K. 82 86
Hurwitz zeta function 97
Hypercube, (k + 1) dimensional 198
Ideals 125 see
Incidence algebra 217
Inclusion-exclusion 139 153 156 218
Inclusion-exclusion, generalized 218
Inclusion-exclusion, truncated 140
INDEX 236—237
Ingham, A.E. 100 102
Intersection 217
Invariant theory 199
inversion 40 -41
Iseki, S. 82 85 86 87
Jackson, F.H. 38 51 52
Jacobi's triple product identity seeTriple product identity
Jacobi, C.G.J. 17 21 30 31 32 49
Join 122 217
Jordan, C. 227 228
Kalckar, F. 227 228
Kendall, M.G. 243 244
Kernel 219
Knopp, M.I. xiii 71 85 87 160 167 177 178
Knuth — Schensted correspondence 179 184—185 187 200
Knuth, D. 179 184 200 212 227 228 230 234 244
Knutson, D. 15 227 228
Kohlbecker, E.E. 100 102
Kolberg, O. 177 178
Kothari, D.S. 228
Kreweras, G. 65 67 199 201
Kronecker -function 217
Labeling 235
Landsberg, G. 227 228
Lascoux, A. 199 201
Lebesgue, V.A. 30 32
Legendre — Jacobi symbol 71
Lehmer, D.H. 86 101 102
Lehner, J. 56 65 66 85 86 101 120 177 178
LeVeque, W.J. 14 15 31 32 65 67 71 87 100 102 118 120 138 158 177 178 200 201 210 211 227 228 244
Lexicographic order 185 187 203 236
Lexicographic order, reverse 232
Linear transformation 225
Linearly independent vectors 213
Linked partition ideals see Partition
Lipschitz summation formula 84
Littlewood, D.E. 227 228
Littlewood, J.E. 68
Livingood, J. 100 102
Logarithmic derivative 98
Long operator 64
Long, C. 65 67
MacDonald, I.G. 200
MacMahon, P.A. xiii 13 14 15 41 42 51 52 57 59 65 67 85 87 100 102 105 137 138 159 177 179 184 189 199 200 201 210 211 227 228 233 234 244
Matrices 184—185 187—188
Maximal element of 219
McKay, J.K.S. 200
Mediant 73
Meet 122 217
Meinardus, G. 88 89 99 100 101 102
Mellin transform 90
Menon, P.K. 31 32
Miller, J.C. p. 243 244
Miller, K.S. 132 138
Minimal element of 219
Mobius function 217?220
Mobius inversion 218 223—224
Mock-theta functions 29—30 82
Mock-theta functions, fifth-order 29—30
Modular equation 161 167 170
Modular form 70 160 177
Modular function 81—82 85—86 160 175 see
Modular group 71 161
Modular transformation 71 82
Modulus 129—131
Moore, E. 15
Motzkin, T.S. 210 211
Multinomial coefficient 215
Multipartite number see also Partition
Multipartite numbers 57 202—203
Multiset 39 126
Multiset, multiplicity in 39
Multiset, permutation 40—42 51 60—61
Murray — Miller algorithm 132
Murray, M. 132 138
Netto, E. 15
Newton's formula 168—169
Nijenhuis, A. 244
Order ideal see Partition
Oscillation see (k i)-positive i)
Ostmann, H.H. xiii 14 15
Parity of p(n) 233
Parkin, T.R. 244
Partial summation 98
Partially ordered set 220 235—237
Partially ordered set, infinite 23 7
Partially ordered set, locally finite 217
Partition 1 212 222 226 243 see Generatng Plane Sets
Partition with congruence conditions 13 14 116—118
Partition with difference conditions 13 14 99 116 118
Partition with distinct parts 2 6 123 156
Partition with odd parts 2 5 13 14 123 237
Partition with parts +1 (mod 5) 109 237
Partition with parts - +2 (mod 5) 109 237
Partition, 51 65 200 227 244
Partition, algorithms 230 244
Partition, analysis 227
Partition, applications of 33 227
Partition, asymptotic formulas 56 68—70 88—89 93 97
Partition, binary 160—161 177
Partition, bipartite numbers 207 -209 243
Partition, Cayley's decomposition 81
Partition, computations for 220ff
Partition, congruences 159—160
Partition, conjugate 7—9 28
Partition, F- 52
Partition, Ferrersgraph 6 13 40 142 214
Partition, flushed 31
Partition, from set H 3 16 100
Partition, functions 12 68 88 97 159—161 237
Partition, generating function 3—4 94 125 139
Partition, graphical representation 6—9 142 145 214
Partition, higher dimensional 179—180 189 197 199 230 234 244
Partition, higher dimensional, Ferrers graph 197—198
Partition, higher dimensional, graphical representation 197 199
Partition, history 244
Partition, ideal equivalence 122—123 128
Partition, ideals 121—125 129
Partition, ideals of order I 121 124—125 207
Partition, identities 17 18 118 121 125 202 207 233
Partition, in combinatorics 212ff
Partition, into powers of m 175—176
Partition, k-dimensional 189 197—199
Partition, k-th excess 50
Partition, lattice structure 122
Partition, linked ideals 128 131 135 137
Partition, linking set 131
Partition, modular 13 14
Partition, multipartite number 57—58 202—204 206 210—21
Partition, multipartite number, distinct parts 203
Partition, multipartite number, odd parts 203
Partition, of infinity 137
Partition, order of ideal 124
Partition, P 235—237
Partition, partial ordering 122
Partition, parts 1
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