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Selected Papers on Discrete Mathematics

Donald E. Knuth (Autor)

Buch | Hardcover

400 Seiten

2001
Centre for the Study of Language & Information (Verlag)
978-1-57586-249-1 (ISBN)

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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.

Donald E. Knuth is one of the world's pre-eminent computer scientists, whose works have had a profound influence on the subject since the publication in 1968 of the first volume of The Art of Computer Programming. Knuth created TeX, a language for typesetting mathematical and scientific texts, and METAFONT, a computer software system for alphabet design. He is professor emeritus at Stanford University.

1. Discussion of Mr. Riordan's paper 'Abel identities and inverse relations'; 2. Duality in addition chains; 3. Combinatorial analysis and computers; 4. Tables of finite fields; 5. Finite semifields and projective planes; 6. A class of projective planes; 7. Construction of a random sequence; 8. Oriented subtrees of an arc digraph; 9. Another enumeration of trees; 10. Notes on central groupoids; 11. Permutations, matrices, and generalized Young tableaux; 12. A note on solid partitions; 13. Subspaces, subsets, and partitions; 14. Enumeration of plane partitions; 15. Complements and transitive closures; 16. Permutations with nonnegative partial sums; 17. Wheels within wheels; 18. The asymptotic number of geometries; 19. Random matroids; 20. Identities from partition involutions; 21. Huffman's algorithm via algebra; 22. A permanent inequality; 23. Efficient balanced codes; 24. The power of a prime that divides a generalized binomial coefficient; 25. The first cycles in an evolving graph; 26. The birth of the giant component; 27. Polynomials involving the floor function; 28. The sandwich theorem; 29. Aztec diamonds, checkerboard graphs, and spanning trees.

Erscheint lt. Verlag	1.6.2001
Reihe/Serie	Center for the Study of Language and Information Publication Lecture Notes ; 106
Verlagsort	Stanford
Sprache	englisch
Maße	152 x 228 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-10	1-57586-249-2 / 1575862492
ISBN-13	978-1-57586-249-1 / 9781575862491
Zustand	Neuware