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Selected Papers on Discrete Mathematics

Sixth 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.

828 pages | 50 line drawings | 6 x 9 | © 2003

Lecture Notes

Computer Science

Mathematics and Statistics

Table of Contents

1. Combinatorial Analysis and Computers
2. Two Notes on Notation
3. Bracket Notation for the ‘Coefficient of’ Operator
4. Johann Faulhaber and Sums of Powers
5. Notes on Thomas Harriot
6. A Permanent Inequality
7. Overlapping Pfaffians
8. The Sandwich Theorem
9. Combinatorial Matrices
10. Aztec Diamonds, Checkerboard Graphs, and Spanning Trees
11. Partitioned Tensor Products and Their Spectra
12. Oriented Subtrees of an Arc Digraph
13. Another Enumeration of Trees
14. Abel Identities and Inverse Relations
15. Convolution Polynomials
16. Polynomials Involving the Floor Function
17. Construction of a Random Sequence
18. An Imaginary Number System
10. Tables of Finite Fields
20. Finite Semifields and Projective Planes
21. A Class of Projective Planes
22. Notes on Central Groupoids
23. Huffman’s Algorithm via Algebra
24. Wheels Within Wheels
25. Complements and Transitive Closures
26. Random Matroids
27. The Asymptotic Number of Geometries
28. Permutations with Nonnegative Partial Sums
29. Efficient Balanced Codes
30. The Knowlton – Graham Partition Problem
31. Permutations, Matrices, and Generalized Young Tableaux
32. Enumeration of Plane Partitions
33. A Note on Solid Partitions
34. Identities from Partition Involutions
35. Subspaces, Subsets, and Partitions
36. The Power of a Prime That Divides a Generalized Coefficient
37. An Almost Linear Recurrence
38. Recurrence Relations Based on Minimization
39. A Recurrence Related to Trees
40. The First Cycles in an Evolving Graph
41. The Birth of the Giant Component

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