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Godsil C. — Algebraic Combinatorics (Chapman Hall Crc Mathematics Series)
Godsil C. — Algebraic Combinatorics (Chapman Hall Crc  Mathematics Series)

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Название: Algebraic Combinatorics (Chapman Hall Crc Mathematics Series)

Автор: Godsil C.

Аннотация:

This graduate level text is distinguished both by the range of topics and the novelty of the material it treats — more than half of the material in it has previously only appeared in research papers. The first half of this book introduces the characteristic and matchings polynomials of a graph. It is instructive to consider these polynomials together because they have a number of properties in common. The matchings polynomial has links with a number of problems in combinatorial enumeration, particularly some of the current work on the combinatorics of orthogonal polynomials. This connection is discussed at some length, and is also in part the stimulus for the inclusion of chapters on orthogonal polynomials and formal power series. Many of the properties of orthogonal polynomials are derived from properties of characteristic polynomials. The second half of the book introduces the theory of polynomial spaces, which provide easy access to a number of important results in design theory, coding theory and the theory of association schemes. This book should be of interest to second year graduate text/reference in mathematics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 368

Добавлена в каталог: 14.03.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
#P-complete problem      124
Addition rule for moment generating functions      153
Addition rule in polynomial space      312
Adjacency matrix      19
Adjugate matrix      52
Affinely equivalent      287
Alternating permutation      170
ARC      22 85 353
Arc function      85
Arc function, normalised      86
Association scheme      177 221 316
Association scheme, dual      249
Association scheme, formally dual      249
Association scheme, imprimitive      232
Association scheme, linear      250
Association scheme, primitive      232
Association scheme, Q-polynomial      229
Association scheme, quotient      233
Association scheme, self-dual      249
Association scheme, symmetric      256
Association scheme, translation      247
Automorphism      243 278 300
Bessel function      159
Bipartite complement      8 353
Bipartite graph      353
Bipartite graph, semi-regular      353
Board      8
Bose — Mesner algebra      223
Cayley graph      245
Cayley graph, linear      246
Cells of partition      75
CHARACTER      243
Character table      243
Characteristic matrix      77
Christoffel numbers      139 140
Christoffel — Darboux identity      60 104 136
Chromatic number      83 353
Code      205
Code, completely regular      208 276
Code, dual      206 299
Code, linear      206 299
Code, perfect      205 336
Code, projective two-weight      257
Code, uniformly packed      212
Cofactor      52
Coherent configuration      256
Complement      4 177 353
Completely regular subset      208 276
Component      354
Coordinate ring      314
Cosine      263
Cospectral graphs      65
Courant — Fischer theorem      84
Covering radius      205 276
Cut-edge      354
CYCLE      354
Degree of code      205
Degree of design      185
Degree set      291
Delsarte clique      276
Derangements      8
Descents      12
Design      184
Design in polynomial space      293
Design, complete      184
Design, quasisymmetric      185
Design, square      185
Design, tight      333
Diameter      354
Dimension of polynomial space      287
Directed graph      354
Directed graph, weighted      56 61
Discrete orthogonality      60 138
Distance matrix      197
Distance-regular graph      82 88 177 195
Distance-regular graph, antipodal      201 265
Distance-regular graph, primitive      201
Distribution matrix      237
Distribution, geometric      169
Distribution, negative binomial      169
Distribution, Poisson      161
Dual degree      205 277
Dual eigenvalues      226
E-code      205
Eigenvalues      225
Euler number      12
EXP      42
Extended conjugacy class      223
Fibre      85 201
Formal power series in k variables      37
Formal power series, composition      41
Formal power series, compositional inverse      41
Formal power series, inverse      40
Formal power series, norm      38
Formal power series, product      37
Formal power series, sum      37
Fundamental group      90
Generating function      45
Generating function, exponential      46 153
Generating function, moment      149
Generating function, ordinary      46
Generating function, walk      46
Geodetic subgraph      269
girth      354
Graph, bilinear forms      196
Graph, Cayley      245
Graph, complete multipartite      353
Graph, conference      180
Graph, covering      85
Graph, directed      354
Graph, distance      201
Graph, distance-Regular      195
Graph, distance-transitive      196
Graph, Grassmann      196
Graph, halved      204
Graph, Hamming      196
Graph, incidence      196 354
Graph, Johnson      196
Graph, Moore      215
Graph, odd      196
Graph, orientation of      119
Graph, Paley      182
Graph, Pfaffian      120
Graph, planar      119
Graph, plane      119
Graph, strongly regular      177 319
Graph, subdivision      353
Graph, walk-regular      81 90 200
Graph, weighted      13 56 61
Grassmann space      290 338
Grassmann space, real      290
Halved graph      204
Hamilton path      107 354
Hamming scheme      289 307 310 319 336
Homomorphism      89
Idempotent      319
Incidence matrix      69
Independent set      353
Index of cover      85
Indicator function      295
Inner distribution      237
Interlacing      29 140
Intersection array      198
Intersection numbers      227
Inverse-dosed      245
Johnson scheme      289 295 307 310 319 323 336
Krein parameters      227 230 322
Length of path      353
LIMIT      39
Line graph      69 353
Linear program      341
local switching      66
LOG      42
Loop      22
MacWilliams transform      237
Matching, perfect      5
Matrix of dual eigenvalues      226
Matrix of eigenvalues      226
Menage problem      9
Minimum distance      205 299
moment      307
Multiplicities      225
n-cube      196
Neighbourhood      353
Number of sign-changes      263
Orderable subset      291
Oriented incidence matrix      69
Orthogonal array      187 319
Orthogonal array, column graph of      188
Orthogonal group      289
Orthogonal polynomials      1 6 60 131
Outer distribution matrix      206
Packing radius      205
Parallel class      343
Partition, column equitable      241
Partition, discrete      75
Partition, distance      82 178 208
Partition, equitable      75 178 195 241
Partition, induced      241
Partition, row equitable      241
Partition, trivial      75
Partition, uniform equitable      210
Path      353 354
Path tree      95
Permanent      123
Permutation group, generously transitive      222
Permutation group, vertex-transitive      81 107
Perron — Frobenius theorem      31 97
Pfaffian      113 114
Polynomial of Meixner type      149 164
Polynomial space      285
Polynomial space, 1-homogeneous      307
Polynomial space, 2-homogeneous      307
Polynomial space, compact      305
Polynomial space, imprimitive      343
Polynomial space, spherical      288
Polynomial, characteristic      1 19 77 93 135
Polynomial, Charlier      160 168
Polynomial, Chebyshev      144 158 309
Polynomial, Gegenbauer      309
Polynomial, generalised Laguerre      168
Polynomial, Hahn      310
Polynomial, Hermite      6 156 167
Polynomial, hit      10 16
Polynomial, inverse      155
Polynomial, Krawtchouk      170 310
Polynomial, Laguerre      157
Polynomial, Legendre      309
Polynomial, matchings      1 68 93 134 144 157
Polynomial, Meixner      169
Polynomial, Meixner — Pollaczek      170
Polynomial, rook      7 9 144 158 168
Polynomial, zonal      286
Polynomial, zonal orthogonal      308
Polynomial, zonal orthogonal, normalised      308
Principal idempotent      27 225
Product, cartesian      127 196 231
Product, direct      89 204 231
Product, Kronecker      230 354
Product, Schur      223
q-binomial coefficient      238
Q-polynomial space      312 333
Quotient of a graph      76
R-anticode      237
R-code      237
r-matching      1
Rank      184
Reconstruction Conjecture      61
refinement      75
Repeated points      288
Representation      24 261
Representation, injective      264
Representation, locally injective      266
Restriction      233
s-distance set      274 291
Schur idempotent      223
Schur-connected      230
Schur-diameter      230
Separation function      285
Sequence of orthogonal polynomials      132
Sequence, log-concave      100
Sequence, moment      149
Sequence, Sheffer      164 165 167
Sequence, Sturm      141
Sequence, unimodal      100
Sign-changes      142
Spectral decomposition      27
Spectral radius      30 69 79 86 125
Sphere-packing bound      238
Spherical embedding      288
Spherical t-design      272
Steiner system      184
Stirling number of the second kind      11 161
Strength of design      185 293
Strength of orthogonal array      187
Strongly connected      354
Strongly regular graph      177 319
Strongly regular graph, imprimitive      177
Strongly regular graph, primitive      177
Strongly regular graph, trivial      177
Subalgebra      234
Subgraph, induced      353
Subgraph, spanning      353
Subscheme      257
Symmetric group      289
Three-term recurrence      4 134
Two-distance set      267
Ultrametric inequality      39
Unit sphere      289 307 311 336
Walk      22 79
Walk of height i      153
Walk, closed      22
Walk, random      68
Walk, reduced      72 90
Walk, tree-like      99 100
Walks      262
Weighted t-design      293
Weighted t-design, support of      293
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