(Paperback)
This volume assembles more than three dozen of Professor Knuth's pioneering contributions to discrete mathematics.
More Reviews and RecommendationsSixth in a series of collected works, Selected Papers on Discrete Mathematics is devoted to Knuth's purely mathematical work. Over forty of Knuth's classic papers spanning the entire range of discrete mathematics are collected in this volume, all brought up to date with extensive revisions and the addition of new material.
The papers emphasize general techniques of problem solving and explore the creation of mathematical patterns. Knuth's prize-winning expositions of mathematical notation, his accounts of episodes in the history of mathematics, and his fundamental papers on tableaux and random graphs are all found here, along with fifty new illustrations. Scholars and students of mathematics will find this an indispensable collection.
| 1 | Combinatorial Analysis and Computers | 1 |
| 2 | Two Notes on Notation | 15 |
| 3 | Bracket Notation for the 'Coefficient of' Operator | 45 |
| 4 | Johann Faulhaber and Sums of Powers | 61 |
| 5 | Notes on Thomas Harriot | 85 |
| 6 | A Permanent Inequality | 89 |
| 7 | Overlapping Pfaffians | 105 |
| 8 | The Sandwich Theorem | 123 |
| 9 | Combinatorial Matrices | 177 |
| 10 | Aztec Diamonds, Checkerboard Graphs, and Spanning Trees | 187 |
| 11 | Partitioned Tensor Products and Their Spectra | 193 |
| 12 | Oriented Subtrees of an Arc Digraph | 203 |
| 13 | Another Enumeration of Trees | 209 |
| 14 | Abel Identities and Inverse Relations | 221 |
| 15 | Convolution Polynomials | 225 |
| 16 | Polynomials Involving the Floor Function | 257 |
| 17 | Construction of a Random Sequence | 265 |
| 18 | An Imaginary Number System | 271 |
| 19 | Tables of Finite Fields | 277 |
| 20 | Finite Semifields and Projective Planes | 305 |
| 21 | A Class of Projective Planes | 345 |
| 22 | Notes on Central Groupoids | 357 |
| 23 | Huffman's Algorithm via Algebra | 377 |
| 24 | Wheels Within Wheels | 387 |
| 25 | Complements and Transitive Closures | 393 |
| 26 | Random Matroids | 405 |
| 27 | The Asymptotic Number of Geometries | 425 |
| 28 | Permutations with Nonnegative Partial Sums | 429 |
| 29 | Efficient Balanced Codes | 433 |
| 30 | The Knowlton-Graham Partition Problem | 439 |
| 31 | Permutations, Matrices, and Generalized Young Tableaux | 445 |
| 32 | Enumeration of Plane Partitions | 465 |
| 33 | A Note on Solid Partitions | 483 |
| 34 | Identities from Partition Involutions | 493 |
| 35 | Subspaces, Subsets, and Partitions | 511 |
| 36 | The Power of a Prime That Divides a Generalized Coefficient | 515 |
| 37 | An Almost Linear Recurrence | 525 |
| 38 | Recurrence Relations Based on Minimization | 537 |
| 39 | A Recurrence Related to Trees | 565 |
| 40 | The First Cycles in an Evolving Graph | 585 |
| 41 | The Birth of the Giant Component | 643 |
| Index | 793 |
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