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Lueneburg H. — Tools and fundamental constructions of combinatorial mathematics
Lueneburg H. — Tools and fundamental constructions of combinatorial mathematics

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Название: Tools and fundamental constructions of combinatorial mathematics

Автор: Lueneburg H.

Язык: en

Рубрика: Математика/Алгебра/Комбинаторика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1989

Количество страниц: 529

Добавлена в каталог: 18.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$A^*$      299
$A^+$      299
$A_5$      280 298
$A_n$      249
$A_X$      250
$A_{Lief$      446
$A_{X,resf$      298
$C_H(x)$      242
$C_l(G)$      121ff
$C_r(G)$      121ff
$C_{\pi,of$      252
$End_F(V)$      427 431
$F^+(A)$      418
$G_R(X)$      432
$G_x$      238
$G_{(i)}$      461
$HL(m_o,\dots,m_n)$      385
$i(\pi)$      247
$length_f$      57
$length_f$, computation of      58
$Lie_R(X)$      446
$L_{fac}(X)$      448
$Mag_R[X]$      464
$Mat_n(K)$      292
$nat_E$      114
$N_G(U)$      244
$pol_R(X)$      432
$pr\ddot uf_V$      229
$P_<$      139
$P_k(S)$      42ff 64
$P_\le$      469
$Sec(S,\le)$      339
$Syl_p(G)$      243
$Sym[x_1,\dots,x_n]$      436
$S_5$      288 298
$S_6$      288 298
$S_X$      246
$S_{X,res}$      251 286
$Term(X,\Omega_1,\Omega_2)$      407f
$U_R(B)$      456
$\omega$      339
$\Omega$-algebra      110
$\Omega$-algebra structure      109
Abelian normal subgroup      298
Active index      150 152f
Addition in a Dedekind triple      22
Addition in a Dedekind triple, associativity of      24
Addition in a Dedekind triple, cancellation law of      24
Addition in a Dedekind triple, commutativity of      23
Additive group of the integers      130
Adjacency list      230 233
Affine geometry      404
Affine subspace      4 04
Affinely independent      404
Algebraically closed      476
Algebraically dependent      405
Algebraically independent      405
Algorithm      See Extra appendix
Alphabet      73 299 415
Alternating group      249f
Alternating group is simple      285
Alternating group, transitivity of      280
Antichain      342ff
Antihomomorphism      113
Arity      109
ASS      415
Assignment problem      391
Associative law      111 417
Atleastk      163
Automorphism      111
Automorphism, inner      288
Automorphisms, group of      284
Average labour      67 69 177 281
Axiom of Choice      352 358 371
B(n)      See Bell numbers
Bell numbers      166 168f 170 203
Bezout Domain      405
bin      58
BINARY      See Operation or Gray code or Representation
Binomial coefficient      43 65
Binomial coefficient, evaluation of      45
Binomial formula      43
BiWi(B)      455
Block of a permutation group      283
Block of an incidence structure      38
Bracketing      416f
Cancellation law      24 27 123 419
Cancellation law, left      24
Cancellation law, right      24
Canonical mapping      429
Cardinal      33
Carrier      110
CART      See Cartesian product
Catalan numbers      4U 426
Cauchy product      4U
centralizer      242
Centre of a group      242
Chain      338
Chain, maximal      338ff 345
char(S)      138
Characteristic      138
Characteristic polynomial      293
Class equation      242
Closed subset      367
Closed under an operation      110
Com      417
Commutator      423 446 459
Commutator subgroup      423
Compatible      110 116
Concatenation      299 415
Congruence      116 117
Conjugacy class      242 278
Conjugate elements      242
Conjugate subgroups      244
Conversion, binary to Gray      89
Conversion, decimal to Gray      96
Conversion, Gray to binary      89
Conversion, Gray to decimal      101
Convex hull      390
Countable      48 54 69 281
Cover      367
Cramer's rule      439 440
Critical subfamily      378 379
CYCLE      See Permutation
Cyclic conjugate      312
D(n,q)      300
Data structure      434
DEC      58
decimal      See Representation
Dedekind numbers      299 300 307f 312 334 451 468
Dedekind triple      13
Dedekind triple operating on a monoid      25ff
Dedekind triple, gcd in a      29
Dedekind triple, homomorphism into a Dedekind triple      29
Dedekind triple, homomorphism into a semiring      29
Dedekind triple, subsets of, are finite or denumerable      54
Dedekind triples are isomorphic      20
Dedekind's recursion theorem      13 15 359
Dedekind's recursion theorem, second proof of the r. t.      19
deg(x)      228
Degree of a polynomial      431
Degree of a vertex      228
Denumerable      48 54 69
Dependence      402
Derivative of a Gray code      211
Derivative of a sequence      211
dev(x)      456
Deviation      456
Direct product      244
Distance      232
Distributive law      26f 112
DIT()      17f 33
DIT(), another description of      21
div      29 55
Divisible      45
Division with remainder      28
Divisor      45
Dobinski      170
dom R      49 64
Domain of positivity      139ff 470
Double counting principle      38 44 228 239 241 345
Doubly stochastic matrix      390
EDGE      227
Elementary abelian      See Group
Elementary symmetric polynomial      435
Embeddable      111
End point      228
End(M)      112 142
End(M), natural      117
Endomorphism      111
Endomorphism ring      112
Epimorphism      111 112
Equipotent      363
Euler's totient function      257f 259 301
Evaluate      417
Evaluation      426
Exponent of a group      142
Exponential numbers      166 203.
f(A)      418
Factor algebra      117
Factor group      117
Factor set      114
Factorial      44
Field      137. See also Subfield
Field of quotients      136 442
Field of rationals      125
Field, algebraically closed      476
Field, finite      54 326.
Field, finite subgroup of its multiplicative group      329
Field, function      44%
Field, ordered      476
Field, splitting      327 328 442
Fin()      47 64
Fin(D) is denumerable      48f
Finite character      356
Finite field      See Field
Finite intersection property      367
Finite set      33ff 52 338 359ff 372 342
Finite set, subset of      34
Finite set, Tarski-      53f
Finite sets, cartesian product of      37
Finite sets, union of      36
Finite skewfield      143
Finite vector space      54
fip(S,T)      367
Fixed element      239
Forest      404
formal Laurent series, field of      444
Formal power series, ring of      444
Free Abelian group      420 423
Free abelian group, $\Omega$-algebra      415
Free abelian group, associative algebra      432
Free abelian group, commutative algebra      433
Free abelian group, commutative semigroup      418
Free abelian group, group      422 474
Free abelian group, Lie algebra      451 452
Free abelian group, R-algebra      431
Free abelian group, R-module      450
Free abelian group, semigroup      417
Free abelian group, term algebra      414 431 444
Frobenius automorphism      327 330 331 333
Frobenius endomorphism      326
Fully invariant subgroup      423
Function      See Extra appendix
Fundamental theorem of algebra      479
fuse(A)      120
Galois field      137 328ff
Gauss' elimination      259
Gauss' numbers      54. See also Dedekind numbers
Generating function      203 411
Generator      328
GF(q)      328
Graph      227
Graph, connected      227 250 251
Graph, connected component of      228 237
Gray code, binary reflected      49 71 145 206 226
Gray code, binary reflected, bisection of      186
Gray code, general      204ff 207 210 225 268
Gray code, general , loopless generation of      217ff
Greatest common divisor      29
Group      112 122 143
group(X)      421
Group, abelian      112 423
Group, abelian, torsion free      472
Group, cyclic      142 328 329
Group, elementary abelian      40 284 298
Group, locally cyclic      143
Group, permutation      See Permutation group
Groupoid      111 121 123 428 443
Groupoid with one      112
Hausdorff's Maximum principle      356 358 362
Homogeneous      447
Homomorphism      29 111 126 132 134 142 348.
Homomorphisms, linearly independent      330
Hull operator      4 04
Ideal      443
Ideal of Z      142
Ideal, left      113
Ideal, principal      142
Ideal, right      113
Incidence structure      37
Incidence structure, finite      37
Incidence structure, isomorphism of      387
Independence structure      401 404f
Index of a subgroup      240
Induction principle      13
Induction versus recursion      14f 38 52
Infective      See Mapping
Infinite set      358 359 362 364
Inn(G)      298
Integral domain      136 131 138 143
inversion      247
Inversion vector      265ff
Inversions, number of      247
Involution      286
Isomorphism      20 111 338 350
Isomorphism theorem, first      118
Isomorphism theorem, second      119
Isomorphism theorem, third      120
Jacobi identity      446
k-subset      42 67 69
kern()      38 114
Kernel      38 114 117
L      48 60S
LD      183
Leading coefficient      431
Lemma of Cauchy — Frobenius      239 278
Lemma of Teichmueller and Tukey      356 358 361 371 401
Length of a finite set      33
Length of a representation of an integer      57. See also word
Lexical      See Order
Lie algebra      446ff
Lie algebra, special      453 455
Linear R-algebra      4%1
Linearly independent      330 356 447
LinInd      54
Little Fermat theorem      241 301
localization      125ff 133
Lower bound      316
Lower central series      461
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