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Ionin Y.J., Shrikhande M.S. — Combinatorics of Symmetric Designs
Ionin Y.J., Shrikhande M.S. — Combinatorics of Symmetric Designs

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Название: Combinatorics of Symmetric Designs

Авторы: Ionin Y.J., Shrikhande M.S.

Аннотация:

A unified and comprehensive exposition of the theory of symmetric designs with emphasis on recent developments.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 520

Добавлена в каталог: 02.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$(m, n, k, \lambda)$-RDS      314
$(n, r, \mu)$-net      106
$(r, \lambda)$-design      154
$(v, k, \lambda)$-difference set      294
$(v, k, \lambda)$-graph      234
$(v, k, \lambda)$-subdesign      407
$(v,b,r, k, \lambda)$-design      24
$A \circ B$      111
$A \otimes B$      67 117
$AG_d(n,q)$      78
$A^T$      16
$A_\mu(s)$      171
$A_{n,2}(q)$      215
$C_n$      19
$D(X_0)$      16
$D(X_0, \mathcal{B}_0)$      16
$D^t$      17
$D^X$      16
$D^Y$      16
$D_x$      16
$d_Y$      16
$GF(q)*$      60
$GF(q)^+$      60
$G_2(d)$-graph      246
$G_23$      199
$G_24$      199
$I_n$      16
$J_n$      16
$J_{m,n}$      16
$K_n$      19
$K_{m,n}$      20
$L_2(n)$      214
$L_r(n)$      214
$NL_r(n)$      215
$PG_d(n,q)$      81
$PL_r(n)$      215
$s \times D$      17
$W_12$      208
$W_22$      201
$W_23$      201
$W_24$      201
$\Gamma(x)$      19
$\GammaL(n, q)$      84
$\lambda$-arc      428
$\lambda$-design      13
$\lambda$-linked design      13
$\mathcal{B}^Y$      16
$\mathcal{B}_Y$      16
$\mathcal{K}(H)$      131
$\omega$-circulant matrix      339
$\overline{xyz}$      87
$\overline{xy}$      61 72
(a, m, t)-BS      307
(a, m,h, +)-EBS      308
(a, m,h, -)-EBS      308
(c, A)-central collineation      75
(c, A)-desarguesian plane      108
(c, A)-elation      75
(c, A)-homology      75
(c, A)-perspectivity      75
(c, A)-transitive plane      108
(n, m, d)-code      98
(n, r)-net      63
0      16
2-$(v, k, \lambda)$ design      28
a, b, x      16
Abelian difference set      294
Absolute point      233
Action of a group      39
Adjacency matrix      20 240
Adjacent vertices      19 240
Affine $\alpha$-resolvable PBD      161
Affine geometry      78
Affine plane      61
Affine resolution      157
AG(n, q)      78
Alphabet      97
Amicable Hadamard matrices      151
Arc of digraph      239
Arc of symmetric design      428
Ascendant      230
Association matrix      248
Association scheme      247
Aut(D)      39
Automorphism group      39
Automorphism of design      39
Axis of collineation      74
Baer partition      412
Baer subdesign      408
Baer subplane      209 408
Balanced generalized weighing matrix      323
Balanced incomplete block design      57
Balanced weighing matrix      366
Balanced weighing system      366
Base blocks      42
BGW      323
BGW with classical parameters      331
BGW$(v, k, \lambda; G)$      323
BH-design      283
Bhattacharya's Example      33
BIBD      57
Binary code      98
Binary Golay code      199
Bipartite graph      19
Biplane      287
Birkhoff theorem      54
Block      14
Block circulant matrix      290
Block complementation      448
Block derived substructure      16
Block graph      252
Block intersection      57
Block schematic design      250
Block section      57
Block set      14
Block size      14
Block-residual substructure      16
Bose — Mesner algebra      249
Bose — Shrikhande-Parker Theorem      68
Bose — Shrikhande-Singhi Theorem      255
Bose's Inequality      156
Bruck subdesign      420
Bruck — Ryser Theorem      74
Bruck — Ryser-Chowla Theorem      37
Building block      307
Building set      307
Burnside lemma      40
Bush-type Hadamard matrix      130
Cameron — Delsarte Theorem      272
Cameron's Theorem      196
Cardinality of a block      14
Cayley table      105
Center of collineation      74
Central collineation      75
Chang graphs      227
Character group      320
Character of group      296
Character of group ring      296
Characteristic polynomial of graph      21
Chen difference set      313
Circulant matrix      290
Class graph      274
Clebsch graph      214
CLIQUE      19
Coclique      19
Codeword      98
Collineation      74 84
Complement of graph      20
Complementary incidence structure      17
Complete block      14
Complete design      25
Complete graph      19
Complete multipartite graph      20
Conference matrix      119
Conjugate element      296
Conjugate matrices      323
Connected component      20
Connected graph      20
Core of BGW matrix      347
Core of conference matrix      120
Covering extended building set      308
CYCLE      19
Cyclic design      401
Cyclic difference set      294
Cyclotomic difference set      300
Cyclotomic scheme      249
D'      17
d-flat      77
Davis — Jedwab difference set      312
de Bruijn — Erdos theorem      452
Degree      19
Degree of net      63
Dembowski — Wagner Theorem      90
Derived design      32
Derived substructure      16
Desargues theorem      85 108
Desarguesian plane      85
Descendant      230
Development of subset      294
Difference set      294
Directed graph, digraph      239
Direction      107
Disjoint union of graphs      20
Divisible difference set      320
Dodecad      208
Dominating vertex      240
Doubly regular tournament      246
Dual code      100
Dual incidence structure      17
EDGE      19
Eigenspace      21
Eigenvalue      21
Eigenvector      21
Elementary Abelian group      60
Embeddable design      254
Embeddable PBD      173
Embeddable quasi-derived design      443
Embeddable quasi-residual design      33
Equidistant code      144
Equidistant family of sets      9
Equivalent codes      98
Equivalent Hadamard matrices      114
Error-correcting code      98
Extended binary Golay code      199
Extension of field      59
Extension of t-design      195
Faithful action      39
Fano plane      5
First Ray — Chaudhuri — Wilson Inequality      3
Fisher's Inequality      26
Fixed block      39
Fixed point      39
Flag      14
Frobenius automorphism      60
Full automorphism group      39
Full collineation group      74
Fundamental theorem of projective geometry      84
G-invariant matrix      289
G-orbit      39
Gaussian coefficient      76
Generalized Bhaskar Rao design      367
Generalized conference matrix      328
Generalized Hadamard matrix      325
Generalized weighing matrix      366
Generator matrix      100
Gewirtz graph      234
GF(q)      59
GH$(G; \lambda)$      325
GL(n, q)      108
Global decomposition      369
GMW-difference set      317
Gordon — Mills — Welch difference set      317
Graph      19
Group divisible designs      320
Group invariant matrix      289
Group of rotations      342
Group of symmetries      302 341 392
Group ring      292
Hadamard 2-design      115 193
Hadamard 3-design      116 187 193
Hadamard difference set      313
Hadamard family      10
Hadamard matrix      9 113
Hadamard product      117
Hadamard series      115 488
Hadamard system      366
Hadamard-Menon difference set      321
Hall — Connor Theorem      254
Hamming Bound Theorem      99
Hamming code      101
Hamming distance      8
Hamming scheme      248
Hamming space      97
Hasse invariant      37
Higman — Sims graph      244
Higman — Sims group      211
Hilbert symbol      35
Hoffman — Singleton graph      221 245
Hyperoval      209
Hyperplane      78
i      16
Incidence matrix      14
Incidence relation      14
Incidence structure      14
Inclusion-Exclusion Principle      187
Independent subdesigns      427
Index of BGW matrix      324
Index of PBD      154
Index of Ryser design      8 447
Induced subgraph      19
Inner product      100
Integrality Condition      220
Intersecting lines      62
Intersection number      3 188
Inversion formula      320
Isomorphic structures      17
j      16
Johnson scheme      248
Kernel of nearfield      328
Kronecker product      117
Kronecker product over group      341
Ladder graph      19
Large Witt designs      198
Latin square      64
Latin square graph      214
Left nearfield      327
Legendre symbol      34
Length of walk      20
Levi graph      19
Line      61 62 72 78 86
Linear code      99
Local decomposition      392
m block nonembeddability condition      431
M-arc      424
M-partition      273
Mann's inequality      54
Maximal decomposition      288
Maximal equidistant code      183
McFarland difference set      311
Mean distance      182
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