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Andrews G.E. — The Theory of Partitions
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Название: The Theory of PartitionsАвтор: 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.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1976Количество страниц: 255Добавлена в каталог: 06.12.2005Операции: Положить на полку |
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Partition, perfect 136—137 Partition, protruded 51 Partition, restricted 33 210 243 Partition, restricted bipartite 207—209 Partition, self-conjugate 14 Partition, sieve methods 139 142 148 153 156 Partition, span 131 Partition, statistical aspects 101 Partition, successive rank 139 153 198 Partition, Sylvestered 30—31 Partition, tables of 237 244 Partition, three dimensional 234 Partition, vector 57 58 patience 59 Pedoe, D. 200 Pentagonal number 10 Pentagonal number theorem 9 11 14 29 202 Percus, J.K. xiii permutations 244 see Plane partition see also Generating function Partition Plane partitions 97 179—180 183—185 188 198—200 236—237 Plane partitions with strict column decrease 188 Plane partitions, asymptotics 199 Plane partitions, conjugate 198 Plane partitions, Ferrars graph 198 Plane partitions, MacMahon's theorem 179 Poincare series 211 Protrusions 51 q-analog, binomial series 17 q-analog, Chu — Vandermonde summation 38 51 q-analog, Gauss's theorem 20 q-analog, Kummer's theorem 20 q-analog, Saalschutz's theorem 38 q-binomial coefficient see Gaussian polynomial q-difference equations 104 121 128 130 132 135 136 q-multinomial coefficient see Gaussian multinomial coefficient q-series see Basic hypergeometric series r-partite number see multipartite number Rademacher, H. xiii 15 68 69 71 85 87 177 178 Radix representation theorem 138 Ramamani, V. 24 31 Ramanuian's conjecture 160 167 170 174 177 Ramanujan's congruence see Ramanjan's conjecture Ramanujan's continued fraction 103 105 Ramanujan, S. 50 68 69 72 85 86 94 101 103 105 109 113 121 123 155 158 159 160 161 167 170 174 177 178 200 Rank 142 175 Rational point 72 Real dimension 63 Reciprocal polynomial 45—48 55 Richmond, B. 100 101 102 Riemann zeta function 83 Riordan, J. xiii 14 15 66 210 211 Robertson, M.M. 211 Robinson, G. deB. 200 201 227 228 Rodseth's theorem 161 165 Roedseth, O. 160 161 165 177 178 Rogen — Szegoe polynomials 50 Rogen — Szegoe polynomials, generating function 49—51 Rogers — Ramanujan identities 50 103 105 109 113 123 155 158 177 200 Rogers — Ramanujan identities, general theorem 118—119 Rogers — Ramanujan identities, Gordon's generalization 109 118 123 156 Rogers — Ramanujan — Schur identities see Rogers — Ramanujan identities Rogers, L.J. 31 32 49 50 52 53 103 105 109 113 118 120 121 123 155 158 177 200 Roselle, D. 65 66 67 210 211 Rota, G.-C. 227 228 229 Roth, K.F. 100 102 Run 60—61 Rutherford, D.E. 199 201 227 229 Saddle point method 89 93 Schensted, C. 184 200 201 Schrutka, L. von 158 Schuetzenberger, M.P. 51 52 65 66 200 201 Schur s partition theorem 116 Schur, I.J. 48 105 116 118 120 158 Schwarz, W. 100 102 Scoville, R. 66 Segment 217—218 220 Selberg, A. 118 120 Semi-ideal see Partition Semi-invariant 48 Sets, inclusion 218 Sets, lattice of subsets 218 Sets, partial order 217 Sets, partition lattice 217 Sets, partition refinement 219 Sets, partitions 212 214—217 220—222 Shanks, D. 244 Sieve methods 139ff see Sieve methods, generalized 218 Simon — Newcomb's problem 54 59—60 65 Singh, V.N. 118 120 Slater, L.J. 31 32 Sloane, N.J.A. 243 244 Snapper, E. 227 229 Solid partitions see Partition Solomon, L. 211 span see Partition stacks 52 Stanley, R.P. 45 51 52 53 65 67 200 201 227 229 244 Star, Z. 65 67 Starcher, G.W. 14 15 Steadily decreasing 207 Stenger, A. 158 Stirling numbers, first kind 219—220 Stirling numbers, second kind 219—220 Strehl, V. 67 Subbararo, M.V. 13 14 15 31 32 138 204 210 211 Subramanyasastri, V.V. 81 85 87 Subspaces 213—214 225 Subspaces, m-dimensional 213 Successive rank see Partition Sum of squares of divisors 237 Summatory maximum 209 Swinnerton-Dyer, H.P.F. 161 175 178 Sylvester, J 1. 15 24 31 32 51 52 53 139 140 Symmetric functions 212 217 221 Symmetric functions, fundamental theorem 221 223—224 Symmetric group 211 Symmetric group, representation theory 199 Szegoe, G. 49 50 52 53 Szekeres, G. 100 101 102 Temperley, H.N.V. 100 101 227 229 Theta functions 105 Tietze, H. 200 201 Topological sequence 235—237 244 Trace 198 210 Trace conjugate 198 Triple product identity 17 21 30 49 108—109 176 Turan, P. 101 102 two-dimensional arrays 179 Unimodal distribution 100 Unimodal polynomial 45—48 55 union 217 Vahlen, K.T. 100 102 158 Valuation, 5-adic 168 Valuation, positive 122 Vector spaces, finite 212 225 227 Vector spaces, graded 211 Venkatachaliengar, K. 24 31 32 Watson, G.N. 31 32 51 53 82 85 87 101 102 105 118 120 160 177 178 Whiteman, A. 87 Wilf, H.S. 244 Wright, E.M. xiii 14 15 32 100 102 200 201 210 211 229 Young tableaux 199 237 Young, A. 199 Zeckendorf's theorem 138 Zeta function of a lattice 217
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