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Knuth D.E. — Selected papers on discrete mathematics
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Íàçâàíèå: Selected papers on discrete mathematicsÀâòîð: Knuth D.E. Àííîòàöèÿ: 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.
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Ïðåäìåòíûé óêàçàòåëü
Desargues, Gerard 317 Desarmenien, Jacques Robert Jeanesarmenien 105 481—482 Desnanot, Pierre 112 114 120 Determinants x 110—114 119 Dickson, Leonard Eugene 306 335—336 341 343 519 523 Difference sets 7—8 Differential posets 186 Differentiation 50 231 656 Difunctional closure 402 Digraphs (directed graphs) xii 357 Digraphs, random 785—788 Digraphs, strong components 395—397 785 Digraphs, strongly connected 387—391 785—788 Digraphs, weak components 395—397 404 Dijkstra Debets, Maria C. 58 Dijkstra, Edsger Wijbe 58 Direct cosum of graphs 145 Direct sum of graphs 143 Directed graphs xii 357 Directed multigraph process 785—788 Dirichlet, Johann Peter Gustav Lejeune, integrals 554 Discrete mathematics x—xii 15 Distributive laws 306 308 309 Distributive quasifield 306 Dixon, Alfred Cardew 53 59 Dmitriev, E.F. 676 788 Dodgson, Charles Lutwidge 112—113 120 Dold, Albrecht 192 202 Doob, Michael 192 202 Dot product 45 124 Dot product of matrices 133 Dot product of tensors 322 Doubly infinite series 45—51 Doubly stochastic matrix 95—98 104 Dowling, Thomas Allan xv 221 Dress, Andreas Walter Martin 119 120 Drew, John Henry 375 Dual argument 361—362 Dual feasible matrix 165 Dual of a planar graph 189 Dual of a projective plane 331—332 Dual tableau 456—457 Dual ternary operation 312—313 344 Duality principle 133 169 Duckworth, Richard 13 Dulmage, Andrew Lloyd 11 Duplication formula 665 699 765 Dwyer, Paul Sumner 303 Dynamic programming 5 526 537 541 Ear decomposition 391 Echelon form 512 Eckmann, Beno 192 202 Edge automorphism 680 Edge-symmetric graph 153 Edmonds, John Robert (= Jack) 405 422 Edwards, Anthony William Fairbank 62 78—79 83 Egervary, Jeno (= Eugen) 96 103 EGF 590 Egorychev, Georgii Petrovich 58 89 94 103—104 Ehresmann, Charles 513 Eigenvalues 92 125 155 182 188 199 Eigenvectors 125 181 185 Eilers, Daniel Ralph xiii Eisenstein, Ferdinand Gotthold Max 567 582 652 789 Elementary Abelian group 308 Elkies, Noam David 187 191 192 Elliptic theta function 494 571 Empirical data 778—780 792 Enlargements 406 408 414—415 Enveloping series 639—640 Equilibrium vector 97 Equivalence relation 395 407 Equivalent hypercubes 326 Equivalent quadratic forms 90—91 Erdelyi, Arthur 37 43 431—432 Erdos, Pal (= Paul) 546 563 585—588 615 618 626 628 641 643—644 647 719 728 789 Erections 423 Esseen, Carl-Gustav 577 Etchemendy, Max xiii Etherington, Ivor Malcolm Haddon 431—432 Euler summation formula 82 572 Euler totient function 295 521 Euler, Leonhard 5 494 498 501 502 509 546 563 710 Eulerian circuits 207—208 Evans, T.A. 8 11 Evans, Trevor 357 359—360 364 371—372 375 Evolution of complex components 644 722 780 Evolution of deficiency 740 Evolving graph 585—792 Ewing, John Harwood 39 44 Excess of a multigraph 646—647 651 703 722 735 740 753 761 763 779 Exp function in finite field 278—279 Expansion formula for 752 Exponent modulo p 280 Exponential generating function 590 exponentiation 88 301—302 Ezekiel, son of Buzi 387 Facets 163 166 170 Factorial powers 30—33 36—38 221 228 232—233 256 731 Factorials 86 Falikman, Dmitry Iechielovich 104 Fano, Robert Mano 12 Farkas, Imre 134 Faulhaber, Johann 61—84 Faulhaber, Johann, portrait 63 Feasible matrix 131 Feller, Willibald (= Vilim = Willy = William) 577 582 Fenchel, Werner 94 103 Fibonacci, Leonardo, sequence 516 520—523 525—527 553—554 Fibonomial coefficients 38 515—516 521 Field polynomial 295 Finite fields xi 277—304 511 Finite Fourier transform 150 First cycle 585—642 759 767 778 792 Fischer, Ludwig Joseph 10 Fishburn, Peter Clingerman 404 FKG inequality 732 Flajolet, Philippe Patrick Michel xii xiii 39 40 44 58 59 570 573 582 585 789 Fletcher, Raymond Russwald, III 375 Floating-point arithmetic 88 Floor function xi 257—264 Flores, Ivan 10 flowchart 273 Foata, Dominique Cyprien xiv 105 Fontaine des Bertins, Alexis 113 Ford, Lester Randolph 44 Ford, Lester Randolph, Jr. 268 270 Forest 622 Formal power series 49 Fortuin, C.M. 789 Four-color problem 5 Fourier, Jean Baptiste Joseph 34 40 Fractional part 257 Franklin, Fabian 481 494—497 502 509 510 513 Franklin, Joel Nick 265 270 Fray, Robert Dutton 515 524 Fredman, Michael Lawrence xiii 537 556 563 Free central groupoids 371—373 Free erections 423 Free relations 397 Free trees 209 217 565 588—591 Frenzen, Christopher Lee 40 Frieze, Alan Michael 788 Frobenius, Ferdinand Georg 153 202 469 480 Furck, Sebastian 63 Gaitman, Amanda Carol 176 Gale, David 441 443 Galois, Evariste, fields xi 277—304 511 Galton, Francis 563 Gamma function 665 689 696 699 710 765 Gapless partition 543 Gardy, Daniele 58 Garey, Michael Randolph 394 402 404 Garsia, Adriano Mario 24 39 40 254 Gauss distribution 577 753 768 Gauss integers 502 Gauss q-nomial coefficients xii 38 511—524 Gauss, Johann Friderich Carl (= Carl Friedrich) 509 510 524 710 GCD 517 522 Gee, Tony xiii Generating function 496 504 546 553 651—653 Generating function, bivariate 591 648—651 Generation of combinatorial patterns 1 Generation of combinatorial patterns, combinations 3 Generation of combinatorial patterns, n-tuples 1 Generation of combinatorial patterns, partitions 3 Generation of combinatorial patterns, perfect matchings 106 117 Generation of combinatorial patterns, permutations 2—3 13 Gessel, Ira Martin 35—36 40 53 58 59 78—79 83—84 244 253 Giambelli, Giovanni Zeno 120 Giant component 589 643—792 Giant strong component 785 Ginibre, Jean 789 Glaser, Anton xiv 41 Glassey, Charles Roger 382 385 Gnewt, Ursula Nom-de-Plume 44 Godsil, Christopher David 192—195 202 Going configurations 622 758 Goldberg, Karl 25 Golden ratio ( 523 Goldman, Jay Robert 513 Golomb, Solomon Wolf 10 270 Golub, Gene Howard 202 Golumbic, Martin Charles 385 Gomes Teixeira, Francisco 236 254 Good, Irving John 209 215 219 248 254 267 270 Gordon, Basil 466—467 471 475—476 480—482 Gouarne, Rene 343 Gould, Henry Wadsworth 35 38 40 219 254 Goulden, Ian Peter 45 59 641 789 Goursat, Edouard Jean-Baptiste 404 Graham Harrison, Susan Lois 422 Graham, Ronald Lewis xiii 28 40 84 254 393 439—441 443 789 Graph process 647 Graph theory x—xiii Grassman, Hermann Gunther 513 Gray, Frank, binary code 2 Greatest integer function 257 Greene, Daniel Hill 41 Groetschel, Martin 123—124 128 174—175 Group 6 306 Group theory ix Guilbaud, Georges Theodule 403 404 Gupta, Hansraj 35 41 Gutman, Ivan 189 192 Hadamard matrix 5 Hadamard, Jacques Salomon 524 Hagen, Johann George 41 Haland Knutson, Inger Johanne xiii 257 264 Half-edge 735—736 745—746 782 Hall, Marshall, Jr. v ix—x xiii 1 7—10 311 343 344 372 377 Hall, Philip 96 103 Hamel, Angele Marie 121 Hamilton, William Rowan, cycles 788 Hamming, Richard Wesley, code 426—427 Hankel symbol 677 Hankel, Hermann, contour 637 689 691 Harary, Frank 203 208 219 641 Hardy, Godfrey Harold 23 41 270 480 494 509 535 Harmonic numbers 531 574 Harmonic numbers, generalized 82—83 Harriot, Thomas 34 85—88 Harris, Bernard 254 Hathaway, Arthur Stafford 510 Hawlitschek, Kurt 84 Hayashi, Harry Sumio 10 Haynsworth, Emilie Virginia 25 Heaviside, Oliver 20 42 Heine, Heinrich Eduard 508 509 Heller, Sidney 546 563 Henrici, Peter Karl Eugen 47 49 59 790 Hensel, Kurt Wilhelm Sebastian 42 Herz, Jean-Claude 304 Higgs, Denis Arthur 425 427 Hindenburg, Carl Friedrich 13 41 History of mathematics 19—22 29—35 44 61—64 68—70 85—88 117—119 502 Hoare, Charles Antony Richard xiv 45 422 Hobby, John Douglas xiii Hodge, William Vallance Douglas 104 Hoffman, Alan Jerome 152 373 Holt Hopfenberg, Anatol Wolf 391 Homogeneous coordinates 8—9 310—312 344 Homomorphism 369 Householder, Alston Scott 125 175 Houten, Lome 466—467 471 475—476 480 Hsu, Leetsch Charles 254 Hu, TE Chiang 381—382 385 Huffman algebra 377 Huffman algorithm xii 377—379 382—383 Huffman, David Albert 385 Hughes, Daniel Richard 11 306 341—343 Hurwitz, Adolf 222—223 Hutchinson, G. 11 Hwang, Frank Kwangming 386 Hypercubes 321-326 Hypergeometric series 221 635 697—698 710—713 721 Hypergeometric series, basic 507—508 Hyperoctahedral group 680 Hyperplane 134 IBM 360/67 computer 414 IBM 7094 computer 364 Ideal primes 518 523 Idempotent elements 360 368 Idempotent mappings 230 Identity element 306 Ikehara, Shikao 561 564 Imaginary number system 271—276 Imaginary part 598 Increasing binary operation 377 Independent set 409—410 420 INDEX function 278—279 Index of a sequence 486—487 Indexing polynomials 279 304 Induced functions 256 Inequalities 731—732 Input/Output 422 Institut Mittag-Leffler 174 186 Integration 656 Interior-point methods 172 Interval arithmetic 88 Interval notation xi Invariant relations 448—449 Inverse of a relation 394 Inversion digraph 452—453 Involutions 480 494—495 503 508 510 Irreducible polynomial modulo p 279—280 Irreducible representation 445 Isolated vertices 588—589 614 704 728 778 780 Isomorph elimination 5 Isomorphism 314 365 Isotopism 313—316 328 348 Itai, Alon 386 Iteration of a function 239—241 Iverson convention 15—25 44 90 Iverson, Kenneth Eugene xi 41 Jabotinsky, Eri 234 237—238 240 244 254 Jackson, David Martin Rhys 45 59 641 789 Jacobi logarithm 283 Jacobi, Carl Gustav Jacob 62 76—77 79 83 84 106 114 117—118 120 303 463 478 494 501—502 505—506 509—510 Jacquet, Philippe Pierre 59
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