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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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Pierce, William A. 7 12 Piff, Michael John 425—427 Pippenger, Nicholas John 564 Pitman, James William 256 Pittel, Boris Gershon xiii 59 255 565 585 628 642—644 653 719 789 790 Planar graphs 189 628 719—720 Plane partitions xii 119 447—448 465—485 Plummer, Michael David 120 Pochhammer, Leo 31 42 Poisson process 605—606 641 Poisson, Simeon Denis, distribution 577 782 Polya, Gyorgy (= George) 493 642 Polynomials 229 Polytope 168 Pope, David Alexander 13 Population growth 87 Poritsky, Hillel 42 Positive semidefinite matrix 132 Postfix notation 238 Poweroids 234 Pragel, Daniel Michael 375 Pre-semifields 308 326 346 Preferential arrangements 238—239 Preservation of order 377 prime factors 190 primitive elements 278 Primitive polynomials 279 Primitive polynomials, modulo p 304 Primitive roots 278 282 Principal isotopes 314 Principle of optimality 541 Proctor, Robert Alan 481 Prodinger, Helmut 641 Projective plane 8—9 333 Projective planes ix 1 6—9 13 310 Projective planes, coordinates for 8—9 310—312 344 Proof of an algorithm 448—449 Proper semifield 307 Propp, James Gary 187 192 Pruefer, Ernst Paul Heinz 210—211 219 223 Pruning a multigraph 677 Psi function 757 Q-nomial coefficients xii 38 511—524 QSTAB 127 161 Quadratic forms 89 Quadratic programming 133 Quater-imaginary number system 271—274 Quaternary number system 272 Queues 383 385 R-classes 368 R-series 49 Radix list sort 421 Raleigh, Sir Walter 85 Ramanujan function 566 569 575 654 673 Ramanujan Iyengar, Srinivasa 506 509—510 535 790 Ramshaw, Lyle Harold 119 Random graph process 587 647 Random graphs xii-xiii 52 585—792 Random multigraph process 587 647 Random objects 4 406 414 Random walk 727 Randomness defined 265 Raney, George Neal 209 219 223—224 Rank in a matroid 411 416 Rank of apparition 518 Real part 598 693 Reciprocity theorem 35—36 Recurrence relations xii 75—78 106 525—583 606—607 696 782 Reduced multigraph 679 Referees 119 191 355 438 Reflective functions 64—67 73—74 Reflexive closure 401 Regular digraphs 207 Regular graphs 152 Regularly divisible sequences 517 522—523 Reiffen, Barney 13 Renewal arrays 238 Renyi, Alfred 569 583 585—588 615 618 626 628 641 643—644 647 654 719 728 789—791 Reversion of series 241 Riddell, Robert James, Jr. 650 791 Riemann, Georg Friedrich Bernhard 561 781 Right nucleus 309 Riguet, Jacques 404 Riordan, John 71 84 209 215 219 221—222 229 237 255 569 583 Robbins, David Peter 113 121 Roberts, Leigh 423 Robinson, D.W. 524 Robinson, Gilbert de Beauregard 447 456 464 Rodemich, Eugene Richard 175 Rodseth, Oystein Johan 546 564 Rogers, Douglas George 255 Rogers, Leonard James 497 509 Roman, Steven 57—59 244 255 Rooted tree 589—591 652 656 Roscoe, Andrew William xiv 45 Rosenstiehl, Pierre 403 404 Rota, Gian-Carlo 244 255 422 425—427 481 513 Rothe, Heinrich August 231 Round-robin tournament 432 Rucinski, Andrzej 641 789 Ruediger, Christian Friedrich 13 Ruler function 528 Rumsey, Howard Calvin, Jr. 113 121 175 Rutherford, Daniel Edwin 464 Ryser, Herbert John 7 9 441 443 S... 22 40 43 Saalschuetz, Louis 53 59 119 121 Sachs, Horst 192 202 Saddle point method 248 598—599 615—616 Sade, Albert 7 12 Salmeri, Antonio 26 43 Samuel, Isaac 343 Samuel, Pierre 304 Sandler, Reuben 12 306 337 343 Sandwich inequality 123 130 Satterthwaite, Edwin Hallowell, Jr. 422 Scheibner, Wilhelm 118 121 Schensted, Craige Eugene (= Ea Ea) 447—449 453 455 457 461—462 464 Schlaefli, Ludwig 33 43 Schloemilch, Oscar Xaver 33 43 Schneider, Ivo 83—84 Schneider, Rolf 94 104 Schoenfeld, Lowell 254 Schoenhage, Arnold 565—566 578 583 642 Schrijver, Alexander 104 123 128 157 173—175 Schroeder, Friedrich Wilhelm Karl Ernst 403 404 Schuetzenberger, Marcel Paul 450 456 464 Schur, Issai 115 121 463 477—478 535 Schwartz, Eugene Sidney 383 386 Science Citation Index 21 94 Scoins, Hubert Ian 217 219 Scott, Dana Stewart 12 Seitz, G. 731 791 Self-loops 648 758—759 786 Semideterminants 118 Semifields 9 305—355 Semipolynomials 674 Semipolynomials of a set 26—27 230 235 395—396 407 439 Sets of lists 239 Shader, Leslie Elwin 373 375 Shadow point 748 781 Shanks, Daniel Charles 500 509 Shannon, Claude Elwood, Jr. 128 175 176 Shears of a semifield plane 317—319 350 Siegel, Carl Ludwig 546 Sign of a permutation 105—108 Sign of a word 106—107 signed 682 Signed permutation 680 Simple weak component 396 Singer, James 8 12 Singular value decomposition 196 Sink vertex 169 Skew symmetry 105 117 Slater, Lucy Joan 791 Slaught, Herbert Ellsworth 1 Smooth multigraph 677 Solid partitions 483—491 Soria, Michele 570 582 Sorting 421 Sosa, Christine xiii Source vertex 169 203 Spanning trees 189—192 Sparse components 671 Sperner theorem 433 Sperner, Emanuel 438 Sprugnoli, Renzo 51 Spuds 135 Stab 127 161 Stable labeling 127 Stable set 127 Staircase 79 Standard deviation 778 Standard form of a hypercube 328 Stanford University 15 83 Stanley, Richard Peter 28 35—36 39 40 43 94 104 186 187 190 192 464 481—482 513 Stanton, Dennis Warren 53 59 186 Stedman, Fabian 13 Steffensen, Johan Frederik 234 255 Stegun, Irene Anne 39 641 Stein, Charles Max 792 Steiner, Jacob, triple systems 5 Stembridge, John Reese 114 119 121 Stenger, Allen 509 Stepanov, Vadim Evdokimovich 570 583 644—645 676 686 719 791 Stieltjes, Thomas Jan, constants 545 Stirling approximation 37 249 426 434 532 571 576 581 649 667 692 717 741—742 766 769 Stirling cycle numbers 25—39 44 87 235 238—239 243 530—532 Stirling numbers, history x 29—35 87 Stirling numbers, notation for 15 25—26 44 Stirling polynomials 245 Stirling subset numbers 25—39 44 71—72 230 235 238—239 243 686 STIRLING, JAMES 25 29—34 37 39 43 Stockmal, Frank 12 Stopping configurations 590 758 Strehl, Karl Ernst Volker 105 Strict plane partitions 465 474—476 Strictly enveloping series 639—640 Strong components 395—397 785 Strong Huffman algebra 383—384 Strong orthogonal labelings 173 Strong product of graphs 146 Strong zero 25 Strongly connected digraphs 387—391 Strongly connected labeled digraphs 785—788 Subbarao, Mathukumalli Venkata 497 510 Subcubes 322 Subspaces 511—513 Sudan, Madhu 174 Sudler, Culbreth, Jr. 466 469 481 510 Summation, repeated 66 Sums of powers 61—84 Sums, manipulation of 16—19 Superpolynomially small 691 SWAC computer 8 Swiercz, Stanislaw 13 Swift, Jonathan Dean 5 10 12 280 303 Switch operation 375 Sylvester, James Joseph 91 114 481 494 502—505 510 511 513 652 791 Symmetric functions 477—479 Symmetric group 445 Symmetric matrices 89 125 447 Symmetrization 404 Szegedy, Mario 174 Szego, Gabor 642 T-graph 210 Tableau algebra 461 Tableaux, generalized Young xii 445—475 477 Tail-exchange method 690 709 Tamaki, Jeanne Keiko 383 385 386 Tanner, Henry William Lloyd 107 109 118 121 Tanner, Rosalind Cecilia Hildegard Young 87 Tanturri, Alberto 546 564 Tarjan, Robert Endre 404 Tauber, Alfred 550 561 581 Taylor, Brook, series 574 777 Taylor, Brook, series, using 752 Taylor, Brook, series, with remainder 639 Teissier, Bernard 94 104 Tensor product of matrices 195 Tensors 321—322 Ternary operation 310—312 Ternary ring 313 TeX iv 31 TH 127 140 161 The Art of Computer Programming 26 124 177 224 256 464 Theory of functions 633—640 Theory versus practice xi 270 Theta function (elliptic) 494 571 Thiel, Larry Henry 13 Thiele, Thorvald Nicolai 34 Thimonier, Loys 58 Thorup, Anders 114 120 Three-legged saddle 602 628 693 742 Tits, L. 62 84 Toll booths 389—390 Tompkins, Charles Brown 5 11 12 Top line 722 729 755 775 Topological sequence 486—488 Topological sorting 486 Torelli, Gabriele 116 121 Torgasev, Aleksandar 192 Toscano, Letterio 256 Total order 396 400 484 649 Trace of a matrix 132 189 Transform, finite 150 Transitive closure 87 393 Translation of a semifield plane 317—319 350 Transpose of a matrix 321 447 455—457 Transpose of a projective plane 331 Transpose of a relation 394 Transpose of a Veblen-Wedderburn system 332 344 Transversals 5 Tree function 229—230 249 590—591 781—782 Tree polynomials 230 233 566—575 653 730—731 Trees 588—591 644 652 704 747—748 760 778 Triangular matrix 89 Triangularization 512 Tricomi, Francesco Giacomo Filippo 37 43 Triplication formula 665 710 765 Trivial component 396 Trotter, Hale Freeman 2 12 13 Trudi, Nicolo 463 Truncation in a matroid 413 Tucker, Alan Curtiss 382 385 Turing, Alan Mathison, machine 21 Tutte, William Thomas 204—205 207 208 212 214 219 405 422 Tweedie, Charles 34 43 Twisted Fields 336 Uhlenbeck, George Eugene 791 Umbral calculus 57 222 255 Understatement 781 Unicyclic components 619 644 652 749 778 779 Uniform model 587 593 647 Uniformly distributed sequences 258 263—270 Unique representation 275—276 University of North Carolina 221 University of South Alabama 83 UNIX 31 Unrooted trees 588—591 644 652 656 704 747—748 760 778
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