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Charalambides C.A. — Enumerative Combinatorics
Charalambides C.A. — Enumerative Combinatorics

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Название: Enumerative Combinatorics

Автор: Charalambides C.A.

Аннотация:

Enumerative Combinatorics presents elaborate and systematic coverage of the theory of enumeration. The first seven chapters provide the necessary background, including basic counting principles and techniques, elementary enumerative topics, and an extended presentation of generating functions and recurrence relations. The remaining seven chapters focus on more advanced topics, including, Stirling numbers, partitions of integers, partition polynomials, Eulerian numbers and Polya's counting theorem.

Extensively classroom tested, this text was designed for introductory- and intermediate-level courses in enumerative combinatorics, but the far-reaching applications of the subject also make the book useful to those in operational research, the physical and social science, and anyone who uses combinatorial methods. Remarks, discussions, tables, and numerous examples support the text, and a wealth of exercises-with hints and answers provided in an appendix—further illustrate the subject's concepts, theorems, and applications.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 609

Добавлена в каталог: 18.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel polynomials      206
Abel’s formula      207
Addition principle      16
Arithmetic progression, sum of terms of      31 194
Ballot numbers      81 230 274
Ballot problem      80 85 100
Banach matchbox problem      85
Bell numbers      97 199 342 474 477
Bell numbers, exponential      199
Beneficial bet      82
Bernoulli numbers      328 329
Binary number system      19 54
Binary sequences, enumeration of      19 36 54
Binomial coefficient (s)      110
Binomial coefficient (s), cycles of      231
Binomial coefficient (s), definition of      112
Binomial coefficient (s), monotonicity of      115
Binomial coefficient (s), orthogonality relation      126
Binomial coefficient (s), recurrence relation of      55 56 59 129
Binomial coefficient (s), table of      56
Binomial convolution formula      115
Binomial generating function      216
Binomial moments of a sequence      215
Bipartitional polynomials, exponential      454
Bipartitional polynomials, general      455
Bipartitional polynomials, logarithmic      457
Bipartitional polynomials, partial      454
Bipartitional polynomials, potential      458
Birthday problem      88
Bonferroni inequalities      154
Booking tickets      20
Boole inequality      155
Boolean algebra      12
Burnside theorem      494
Caravan in the desert      180
Cardinal of a set      14
Carlitz numbers      537
Carlitz numbers, definition of      523
Carlitz numbers, explicit expression of      523
Carlitz numbers, expressed by the generalized factorial coefficients      528
Carlitz numbers, generating function of      527
Carlitz numbers, limiting expression of      529
Carlitz numbers, non-central      539
Carlitz numbers, recurrence relation of      524
Carlitz numbers, table of      526
Carlitz polynomial      525
Carlitz-Riordan numbers of the first kind      329
Carlitz-Riordan numbers of the second kind      330 543 544
Cartesian product      5
Cashier problem      81
Catalan numbers      81 100 196 229
Catalan numbers, convolution of      229
Catalan numbers, generating function of      197
Catalan numbers, recurrence relation of      196
Catalan numbers, table of      196
Cauchy identity      465 481
Cauchy numbers      327 329
Cauchy’s binomial convolution formula      115
Cayley identity      481
Characteristic equation      239
Chebyshev polynomials of the first kind      449
Chebyshev polynomials of the second kind      450
Circular permutation(s)      92 462
Circular permutation(s), enumeration by successions      181 183
Circular permutation(s), succession of      181
Coefficients of the generalized factorials      345
Coefficients of the generalized factorials, associated      367
Coincidence numbers      173
Coincidence numbers, generating function of      219 222
Coincidence numbers, table of      173
Coincidences, double      186
Coincidences, generalized problem      188
Coincidences, multiple      187
Coincidences, number of      173
Coincidences, problem      173
Coloring(s) of a cube      496 506
Coloring(s) of a roulette      510
Coloring(s) of enumeration of      500
Coloring(s) of model of      499
Coloring(s) of the elements of a set      499
Coloring(s) of weight of      501
Combination (s) with limited repetition generating function for the number of      211
Combination (s) with repetition definition of      51
Combination (s) with restricted repetition enumeration of      139 144 164 504
Combination (s), definition of      51
Combination (s), enumeration of      58
Combination (s), general generating function for the number of      209
Combination (s), generating function for the number of      210
Combination (s), recurrence relation for the number of      59
Compositions of integers      401 511
Compound bivariate discrete distributions      456
Compound discrete distributions      422
Connection of cumulants and moments      426 457
Connection of ordinary and factorial moments      285
Convolution of a logarithmic distribution      287
Convolution of sequences      194
Correspondence      7
Coupon collector’s problem      151 313
Cycles of binomial coefficients      231
De Morgan’s formulae      12
Decomposition of a product of primes into factors      347
Delannoy numbers      274
Derangement(s), definition of      170
Derangement(s), number of      170
Derangement(s), recurrence relation for the number of      171
Derivatives of a composite function      420 453
Difference equation      22
Dinner choices in a Chinese restaurant      418
Display of flags on poles      60
Distribution of shares      83 262
Distributions of balls of general specification into distinguish, ordered urns enumeration of      348 349
Distributions of balls of general specification into distinguishable urns enumeration of      350—352
Distributions of balls of generating function of the number of      356
Distributions of distinguishable balls into distinguishable urns enumeration of      48 340 341
Distributions of indistinguish balls into distinguishable urns      60
Distributions of students in sections      67
Distributions, connection with integer solutions of a linear equation      71
Distributions, enumeration of      54 343— 345
Distributions, generating function of the number of      355
Division (s) of a finite set, definition of      13
Division (s) of a finite set, enumeration of      62 97 124 149
Division (s) of a finite set, recurrence relation for the number of      64
Double coincidences      186
Down-up permutations      543
Duration of a series of drawings      175
Elementary symmetric functions      192 427 432 458
Elements in a given number of exchangeable sets, enumeration of      143 147 148
Elements in a given number of sets, enumeration of      137 145 148
Elements in a union of exchangeable sets, enumeration of      142
Elements in a union of sets, enumeration of      132 134
Elements of a given rank      156
Elements of a given rank, enumeration of      156 157
Elevator passengers’ discharge      67 91 133
Equivalence class      493
Equivalence relation      7
Equivalent sets      9
Euler numbers      514 543
Eulerian numbers      530
Eulerian numbers, definition of      514
Eulerian polynomial      516
Euler’s function      140 491 497 498 506 510 511
Euler’s function, table of      140
Euler’s identity      393 402
Euler’s pentagonal theorem      389
Euler’s recurrence relation for sub-factorials      171
Exchangeable sets      142
Explicit expression of      515
Expressed by non-central Stirling numbers of the second kind      539
Expressed by non-central, recurrence relation of      516
Expressed by non-central, symmetric      514
Expressed by non-central, table of      517
Expressed by Stirling numbers of the second kind      519
Expressing power series      520
Expressing sample moments      521
Expressing sample moments, generating function of      518
Expressing sample moments, non-central      538
Faa di Bruno formula      420
Faa di Bruno formula, generalization      434
Factorial      43 104
Factorial convolution formula      105
Factorial generating function      216
Factorial moments of a sequence      215
Factorial, central      329
Factorial, falling      105
Factorial, rising      105
Factors of a positive integer, enumeration of      19 37
Family of elements      8
Fibonacci numbers      74 100 101 253 269 401
Fibonacci numbers of order s      269
Fibonacci numbers, convolution of      271
Fibonacci numbers, generalized      270
Fibonacci numbers, generating function of      254
Fibonacci numbers, table of      254
Formation of committees      352 353
Frechet inequality      166
Function      7
Galilei problem      92 161
Gambler’s ruin      242
Gambler’s ruin, expected time to      246
Gauss — Jacobi identity      394 402
Gegenbauer polynomials      450
Generalized factorial coefficients      152 165 307 312 344 345 347
Generalized factorial coefficients in terms of Stirling numbers      304
Generalized factorial coefficients, associated      166 326 327 366
Generalized factorial coefficients, asymptotic expression of      323
Generalized factorial coefficients, definition of      302
Generalized factorial coefficients, explicit expression of      306
Generalized factorial coefficients, generating function of      305
Generalized factorial coefficients, limiting expression of      307
Generalized factorial coefficients, non-central      318 319 334 540
Generalized factorial coefficients, orthogonality relation      308
Generalized factorial coefficients, recurrence relation of      309 310
Generalized factorial coefficients, table of      311
Generating function for the number of combinations      193 209
Generating function for the number of permutations      193 210
Generating function, binomial      201 216
Generating function, exponential      194
Generating function, factorial      201 216
Generating function, general form of      200
Generating function, moment      216
Generating function, multivariate      219
Generating function, ordinary      194
Genocchi numbers      544
Geometric progression, sum of terms of      21 33
Gould polynomials      207
Gould — Hopper numbers      318
Gould’s formula      208
Group of permutations      489
Group of permutations, alternating      490
Group of permutations, cycle indicator of      489
Group of permutations, cyclic      491
Group of permutations, identity      489
Group of permutations, symmetric      489 490
Gumbel inequality      166
Hanoi tower, transfer of      238
Hermite polynomials      449
Hermite polynomials, generalized      449
Homogeneous product sum symmetric functions      432 458
Inclusion and exclusion principle      134 136
Inclusion and exclusion principle, general expression of      145
Inequalities of Bonferroni      154
Inequality of Boole      155
Inequality of Frechet      166
Inequality of Gumbel      166
Integer solutions of a linear equation      68
Integer solutions, distinguishable urns      71
Integer solutions, enumeration of      69—71 98 138
Inverse map      8
Inverse relation      7
Inverse relations      284
Inversion of power series      437 438
Inversions of permutations      541
Lagrange inversion formula      435
Lagrange series      205 439
Laguerre polynomials      449 452
Lah numbers      302
Lah numbers, non-central      335
Lah numbers, signless      302
Lattice paths      75
Lattice paths with diagonal steps      100
Lattice paths, enumeration of      76—78
Lattice paths, figure      77
Leibnitz numbers      127 275
Lucas numbers      75 270
Lucas numbers of order s      270
Lucas numbers, generalized      271
Maclaurin power series      202
Magic squares      1
MAP      7
Map, bijective      7
Map, identity      8
Map, injective      7
Map, inverse      8
Map, surjective      7
Mean of a sequence      215
Menages numbers, reduced      142
Menages numbers, table of      142
Menages problem      140
Menages problem, modified      163
Menages problem, straight table      163
Mobius function      166
Mobius inversion formula      167
Models of necklaces      498 511
Moment generating function      216
Moments of a sequence      215
Money-changing problem      383
Monomials in a polynomial, enumeration of      99
Morse code      36 346
Multinomial coefficient(s)      123
Multinomial coefficient(s), generating function of      222
Multinomial coefficient(s), recurrence relation of      64
Multinomial coefficient(s), sum of      150 165 400
Multinomial formula      123
Multiple coincidences      187
Multiplication principle      20
Multivariate generating function      219
Newcomb’s problem      513
Newton factorial series      204
Newton’s formula, binomial      111
Newton’s formula, general binomial      115
Newton’s formula, negative binomial      112
Noerlund — Bernoulli numbers      328
Null set      3
Number system of base      5 159
Number system, binary      19 54
Number system, quaternary      224
Number system, ternary      47
Occupancy problem      339
Occupancy problem, classical      340
Operator $\Psi=t\Delta$      286
Operator $\Theta=tD$      286
Orbit      493
Orbit, enumeration of the elements of      494
Order relation      7
Ordered n-tuple      5
Ordered pair      5
Parcelling out procedures      228
Partial derivatives of a function, number of      99
Partial sums, generating function of      255
Partition (s) of a finite set definition of      14
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