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Knuth D.E. — Selected papers on discrete mathematics
Knuth D.E. — Selected papers on discrete mathematics



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Название: Selected papers on discrete mathematics

Автор: Knuth D.E.

Аннотация:

Donald Knuth's influence in computer science ranges from the invention of literate programming to the development of the TeX programming language. One of the foremost figures in the field of mathematical sciences, his papers are widely referenced and stand as milestones of development over a wide range of topics. This volume assembles more than three dozen of Professor Knuth's pioneering contributions to discrete mathematics. It includes a variety of topics in combinatorial mathematics (finite geometries, graph theory, enumeration, partitions, tableaux, matroids, codes); discrete algebra (finite fields, groupoids, closure operators, inequalities, convolutions, Pfaffians); and concrete mathematics (recurrence relations, special numbers and notations, identities, discrete probability). Of particular interest are two fundamental papers in which the evolution of random graphs is studied by means of generating functions.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 826

Добавлена в каталог: 14.06.2015

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$0^{0}$      22
$\alpha(G)$ (stability number)      129
$\beta$-ary partitions      543 546
$\chi (G)$ (chromatic number)      123 130
$\kappa (G)$ (q-stability number)      129
$\Lambda (A)$ (largest eigenvalue)      131
$\mathfrak{J}$ (imaginary part)      598
$\mathfrak{R}$ (real part)      598 693
$\omega (G)$ (clique number)      123 130
$\phi$ (golden ratio)      554
$\pi$ (circle ratio), as data source      408—409 587—588
$\pi$ (circle ratio), mnemonic for      87
$\vartheta (G)$ (Lovasz number)      x 123 129
$\vartheta$ operator for differentiation      51 251—252 619 655 735
$\vartheta$ operator for differentiation, Taylor series analog      752
0-1 matrices      360 439—441 446 480 482
1-Factor      104 see
3-dimensional matrices      321
Abel, Niels Henrik      222—223
Abel, Niels Henrik, binomial theorem      xi 218 222—224
Abeles, Francine Forte      120
Abelian group      6 8
Abelian group, elementary      308
Abl      160
Abramowitz, Milton      39 641
Absolute value      20
Acyclic components      652
Aczel, Janos      381 385
Addition      273
Adjacent vertices      126
Agarwal, Ratan Prakash      501 509
Airy, George Biddle, function      635 638 696—697 767
al-Uqlidisi, Abu al-Hasan Ahmad ibn Ibrahim      88
Alanen, Jack David      xiii 277
Albert, Abraham Adrian      303 306 317—318 336 343 348 355
Aldous, David John      792
Aleksandrov, Aleksandr Danilovich      94 103—104
Algoet, Paul      119
ALGOL 60 language      487—488
ALGOL W language      414 416 422
Alizadeh, Farid      172 174
Almost surely      588
Alon, Noga      438
Alternating sign matrices      113
Andre, Antoine Desire      438
Andrews, George W. Eyre      38 39 481 497 501 508 509
Annulus      47
Anti-isomorphism      331 368
Anti-reflective functions      64—67 73—74
Antiblocker      160
Antisymmetric function      477
APL language      16 24
Appell, Paul Emile      253
Arbogast, Louis Francois Antoine      570
Arc digraph      203
arcsin      236 711
Arora, Sanjeev      174
Art of Computer Programming      26 124 177 224 256 464
Askey, Richard Allen      508 509 788
assertions      448—449
Associated Stirling number      253
Associative inequality      377
Associative law      322—324
Asymmetrization      404
Asymptotic growth      248—253 425—426 526—534 545—563
Asymptotic series      36—37 82 638—640 713 772
Atkin, Arthur Oliver Lonsdale      480 489 563
Austin, Thomas LeRoy, Jr.      217 219
Automorphisms      153 307—308 314 350
Autotopisms      316—319 329 333 350
Aztec diamond      187
b-ary sequence      266
Babbage, Charles      40
Bachmann, Paul Gustav Heinrich      516 523
Backtracking      3—5 487—488 792
Backward difference      64
Bagaev, Gennadii Nikolaevich      653 676 788
Balanced codes      433—438
Balanced digraph      207
Ball, Walter William Rouse      9
Basic (m,t) set      179
Basic hypergeometric series      507—508
Basis of a vector space      511—513
Basis set of a matroid      409—410
Bauer, Henry Raymond, III      422
Baumert, Leonard Daniel      10
Becker, Sheldon      422
Bell numbers      230 235
Bell, Eric Temple      253
Bellman, Richard Ernest      9
Bender, Edward Anton      xiii 464 465 481 489 788
Bendix, Peter Bernard      372
Berge, Claude      162 403
Bergmann, Ernest Eisenhardt      438
Bernoulli polynomials      77—82
Bernoulli trials      577
Bernoulli, Jacques (= Jakob = James), numbers      23 75 79—82 245
Berry, Andrew Campbell      577
Bessel, Friedrich Wilhelm, functions      635 677 697—698 767
beta function      605
Bezout, Etienne      113
Bgf      591 648
Bi-imaginary system      274—276
Bicyclic components      618—622 652 699 761
big bang      646
Bijection      210—213 223 433 451—452 456 458 466—470 485—486 510 543—544
Binary number system      85—88 521 528
Binary partitions      525—526 546
Binary semifields      333 337 349 355
Binary trees      228 377 541—542
Binet, Jacques Philippe Marie      732
Binomial coefficient      225
Binomial coefficient, generalized      xii 38—39 511—524
Binomial power series      81 228 236 246 249
Binomial theorem      225
Binomial theorem, generalized      xi 218 222—224
Binomial type      233—234
Bipartite graphs      x 104 110 119 187—188 627
Birch, Bryan John      563
Birkhoff, Garrett      96 103
Bits variables      416
Bitwise operations      416
Bivariate generating function      591 648—649
Bixby, Robert Eugene      423
Blackburn, John E.      425 427
Blaha, Stephen      472 480
Blaschke, Wilhelm      114
Block designs      7 177
Boethius, Anicius Manlius Torquatus Severinus      86
Bollobas, Bela      174 585 606 641 644—645 778 788
Borchardt, Carl Wilhelm      191 219 652 789
Bose, Bella      438
Bose, Raj Chandra      xv 9 221
Bound variables      51
Bracket notation      45—59 226 590 649
Brackets versus parentheses      24
Bratley, Paul      480 489
Brent, Richard Peirce      253
Brill, John      118 119
Brillhart, John David      303
Brioschi, Francesco      119
Britikov, Vladimir Evgen'evich      708 789
British Museum      x 34 85—86
Brown, Kimberly Ann Lewis      xiii
Brown, Robert, motion      792
Bruck, Richard Hubert      7 9
Bruhat, Francois      481
Brylawski, Thomas Henry      422—423
Bubble sort      571
Bumping      449
Burnside, William Snow, problem      ix
Burroughs 220 computer      333
Burroughs B5000 computer      534
Burroughs Corporation      534
Buseman, Herbert      94 103
Bussey, William Henry      277 303
Cajori, Florian      43
California Institute of Technology      ix
Cambridge University      83
Cancellation law      383
Cancelling a multidigraph      787
Cancelling a multigraph      679
Canfield, Earl Rodney      788
Cantor, Georg Ferdinand Ludwig Philip, ternary set      551
Capelli, Alfredo      256
Carlitz, Leonard      244 254 480 508
Carmichael, Robert Daniel      516 523
Carries      515 519—521
Carter, John Lawrence      13
Cartesian product of graphs      201
Case Institute of Technology      303
Catalan, Eugene Charles, numbers      80 228—229 236
Cauchy inequality      124 137—138 162
Cauchy integral formula      593 692
Cauchy, Augustin Louis      22 40 464 732
Cayley graph      201
Cayley, Arthur      117—119 209 217 219 238 254 546 563 652 789
Central factorial numbers      71 229 237
Central groupoids      357—375
Certificate      139
Chakravarti, Indra Mohan      9
Champernowne, David Gawen      267 270
Characteristic labeling      127
Characteristic of a semifield      308
Characteristic polynomial      188 195 361
Chaundy, Theodore William      480
Checkers      187
Cheema, Mohindar Singh      466 480
Child, James Mark      88
Chinese ring puzzle      2
Chou, Jim Chih-Chun      xiii
Chow, Timothy Yi-Chung      192
Chromatic number of a graph      123 524
Churchhouse, Robert Francis      304 546 563
circles      87
Circuit in a matroid      410 420
Circulant matrix      151
Circular list      416
Ciucu, Mihai      192
Classroom example      357
Clausen, Thomas      23
Clean multigraph      646 743
CLIQUE      123
Clique labeling      127
Closed subsets      406
Closure in a matroid      406
Closure reflexive      401
Closure transitive      87 393
Closure, difunctional      402
Clutter      413—414 423
codes      5 433—438
Cohn, Martin      10
Collineations      314 350
Coloring a graph      123 524
Column vectors      124
Combinations      86
Combinatorial geometries      408 425
Combinatorial matrices      x 177—186
Common eigenvectors      159 186
Commutative law      377—378
Commutative semifields      334 336 345—355
Commutators      ix
Companion matrix      296
Compatible marriages      96
Compatible matrices      157
Compatible partitions      199
Compensation factor      648 678 680 785
Complement of a graph      123
Complement of a relation      393
Completely equidistributed sequence      265—270
Completing the square      90
Complex component      644 657
Complex multigraph      654
Complex partition      502—505
Complex variable theory      633—640
components      570 650
Components acyclic      652
Components bicyclic      618—622 652 699 761
Components complex      644 657 722 780
Components giant      589 643—792 785
Components sparse      671
Components strong      395—397 785
Components trivial      396
Components unicyclic      619 644 652 749 778 779
Components weak      395—397 404
Composition of functions      55 238
Composition of relations      393
Computer science versus mathematics      x
Computers in mathematical research      1—13 345
Comtet, Louis      238 254 641
Concrete Mathematics      15 24 28 84 564
Condensation method      112
Cone      133—134
Confluent hypergeometric series      638 666 773
Conjugates      190—191
Connected multigraph      650—651 761 780
Connected relation      395
Continued fraction      677 782
Continuous mathematics      xi 15
Converse of a relation      394
Convex combination      95—96
Convex corner      160
Convex function      538—539
Convolution family      225—227
Convolution matrix      234 238
Convolution minimization      538
Convolution polynomials      225—256 569
Conway, John Horton      304
Coppersmith, Don      438
Coproduct of graphs      147
Cordero Brana, Minerva      344
Core of a multigraph      678
Corless, Robert Malcolm      256
Coset      359
Cost of a vector      127
Cotrees      191
Coupon collector's problem      57
Covering relation      180 407
Coxeter, Harold Scott Macdonald      9
Cramer, Gabriel      117
Crapo, Henry Howland      422—427
Crelle, August Leopold      20 222
Croft, William James      xiii
Culik, Karel      191
Cunningham, Allan Joseph Champneys      303
Curtis, Frank Edward      375
Cvetkovic, Dragos Mladen      189 192 202
CYCLE      210
Cycle, first      585—642 759 767 778 792
Cyclic group      295
Cyclic shift      429
Cyclotomic number field      190
Cyclotomic polynomials      299 521
de Bruijn, Nicolaas Govert      203 207—208 538 545—546 563 641
de Fermat, Pierre, little theorem      281
de Finetti, Bruno      44
de Laplace (= de la Place), Pierre Simon, Marquis      690
Decomposable matrix      97
Deficiency of a multigraph      646—647 714 729 735 740 753
Delsarte, Philippe      176
1 2 3 4 5
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