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Knuth D.E. — Selected papers on discrete mathematics
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Название: Selected papers on discrete mathematicsАвтор: 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: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2001Количество страниц: 826Добавлена в каталог: 14.06.2015Операции: Положить на полку |
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22 129 543 546 123 130 129 131 598 598 693 123 130 554 408—409 587—588 87 x 123 129 51 251—252 619 655 735 752 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
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(stability number) 
-ary partitions 
(chromatic number) 
(q-stability number) 
(largest eigenvalue) 
(imaginary part) 
(real part) 
(clique number) 
(golden ratio) 
(circle ratio), as data source 
(Lovasz number) 
operator for differentiation 
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