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Ramirez Alfonsin J.L. — Diophantine Frobenius Problem
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Название: Diophantine Frobenius Problem
Автор: Ramirez Alfonsin J.L.
Аннотация: During the early part of the last century, Ferdinand Georg Frobenius (1849-1917) raised the following problem, known as the Frobenius Problem (FP): given relatively prime positive integers a1,,an, find the largest natural number (called the Frobenius number and denoted by g(a1,,an) that is not representable as a nonnegative integer combination of a1,,an.
At first glance FB may look deceptively specialized. Nevertheless it crops up again and again in the most unexpected places and has been extremely useful in investigating many different problems. A number of methods, from several areas of mathematics, have been used in the hope of finding a formula giving the Frobenius number and algorithms to calculate it. The main intention of this book is to highlight such methods, ideas, viewpoints and applications to a broader audience.
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Рубрика: Математика /
Статус предметного указателя: Готов указатель с номерами страниц
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Год издания: 2006
Количество страниц: 250
Добавлена в каталог: 22.05.2008
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Предметный указатель
Apery set 149
Balls and cells problem 175
Basis 1
Basis, Hilbert 132
Basis, regular 62
Bell's method 78
Bernoulli numbers 112 198
Code, algebraic geometric 171
Code, designed minimum distance, Feng — Rao 173
Code, designed minimum distance, Goppa 173
Code, evaluation 173
Code, evaluation, dual 173
Conjugate power equation 178
Convex set 91
Covering radius 22
Cubature formula 179
Cubature formula, m-property 179
Cube-figure 7
Cutting stock problem 96
Davison's algorithm 5
Decision problem 185
Dedekind sums 95
Denumerant 72
Ehrhart polynomial 92
Ehrhart polynomial, reciprocity law 92
Frobenius, directed graph 12
Frobenius, minimal graph 15
Frobenius, number 1
Frobenius, problem FP 1
Function, Kronecker delta 153
Function, Mobius 153
Function, partition 71
Function, subadditive 55
Gomory cuts 67
Gorenstein condition 107
Graded, Hilbert syzygy Graded, theorem 196
Graded, resolution 196
Graph, connected 194
Graph, cycle 194
Graph, F-Harniltonian 182
Graph, Hamiltonian 181
Graph, homogenously traceable 182
Graph, hypo-Hamiltonian 181
Graph, path 194
Graph, Petersen 181
Graph, strongly connected 194
Graph, traceable 182
Greenberg's algorithm 18
Heap and Lynn method 11
Hilbert, function 197
Hilbert, serie 197
HNN group 178
Johnson integers 42
Jugs problem 114
Kannan's method 21
Killingbergtro's algorithm 6
Knapsack, problem 53
Knapsack, problem, integer 25
Liveness problem 162
Matrix, dominating 157
Matrix, graded 196
Matrix, index of primitivity 11 202
Matrix, irreducible 11 200
Matrix, mixed 157
Matrix, non-negative 11
Matrix, permutation 200
Matrix, positive 11
Matrix, primitive 11
Matrix, reducible 11 200
Maximal lattice free body 8
Modular change problem 124
Module 194
Module, free 195
Module, graded 195
Module, projective 195
Module, regrading 195
Module, shift 196
Money-changing problem 1
Monoid 55
Monomial curve 142
Nijenhuis' algorithm 19
Partition vector space problem 165
Petri net 161
Pick's theorem 32
Place/transition net 161
Place/transition net, pure 162
Place/transition net, system 162
Place/transition net, system, dead 162
Place/transition net, system, live 162
Place/transition net, system, weighted circuit 163
Polygon, lattice 32
Polygon, simple 32
Polytope, convex 91
Polytope, face 92
Polytope, facet 92
Polytope, integral 92
Polytope, rational 92
Postage Stamp Problem 127
Postage stamp problem, global 133
Pseudo-conductor 130
Pseudo-conductor, m-conductor 133
Quantifier elimination 45
Quasipolynomial 93
Random vector algorithm 180
Rodseth's algorithm 3
Scarf and Shallcross' algorithm 9
Semigroup 135
Semigroup 7-liyperelliptic 154
Semigroup, Arf numerical 156
Semigroup, Buchweitz 155
Semigroup, complete intersection 152
Semigroup, conductor 135
Semigroup, critical number 157
Semigroup, derived 146
Semigroup, embedding dimension 135
Semigroup, free 140
Semigroup, gaps 135
Semigroup, gaps, fundamental 155
Semigroup, genus 135
Semigroup, hyperelliptic 140
Semigroup, irreducible 148
Semigroup, multiplicity 135
Semigroup, non-gaps 135
Semigroup, numerical 135
Semigroup, pseudo-symmetric 146
Semigroup, ring 87
Semigroup, Schubert index 156
Semigroup, symmetric 141
Semigroup, telescopic 139
Semigroup, toric ideal of 197
Semigroup, type 142
Semigroup, Weierstrass 154
Sequence, almost chain 29
Sequence, almost Sequence, arithmetic 29
Sequence, arithmetic 59
Sequence, chain 29
Sequence, chain-divisible 98
Sequence, flat 58
Sequence, independent 38
Sequence, pleasant 127
Sequence, saturated 122
Sequence, strongly flat 58
Sequence, superincreasing 98
Sequence, telescopic 139
Sequence, type of 151
Shell-sort method 159 197
Skupien's algorithm 125
Sylver coinage game 113
Tessalation 174
Tiling 174
Turing reduction 194
Unimodular zonotope 92
Wilf's algorithm 19
Zorn's lemma 143
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