Implementing Discrete Mathematics
Perseus Books (Verlag)
978-0-201-69467-3 (ISBN)
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This book concentrates on two distinct areas in discrete mathematics. The first section deals with combinatorics, loosely defined as the study of counting. We provide functions for generating combinatorial objects such as permutations, partitions, and Young tableaux, as well as for studying various aspects of these structures.The second section considers graph theory, which can be defined equally loosely as the study of binary relations. We consider a wide variety of graphs, provide functions to create them, and functions to show what special properties they have, Although graphs are combinatorial structures, understanding them requires pictures or embeddings. Thus we provide functions to create a variety of graph embeddings, so the same structure can be viewed in several different ways. Algorithmic graph theory is an important interface between mathematics and computer science, and so we study a variety of polynominal and exponential time problems.
Permutations and Combinations Permutations Permutation Groups Inversions and Inversion Vectors Special Classes of Permutations Combinations Exercises and Research Problems * Partitions, Compositions, and Young Tableaux Partitions Compositions Young Tableaux Exercises and Research Problems * Representing Graphs Data Structures for Graphs Elementary Graph Operations Graph Embeddings Storage Formats Exercises and Research Problems * Generating Graphs Regular Structures Trees Random Graphs Relations and Functional Graphs Exercises and Research Problems * Properties of Graphs Connectivity Graph Isomorphism Cycles in Graphs Partial Orders Graph Coloring Cliques, Vertex Covers, and Independent Sets Exercises and Research Problems * Algorithmic Graph Theory Shortest Paths Minimum Spanning Trees Network Flow Matching Planar Graphs Exercises and Research Problems
| Verlagsort | Boulder |
|---|---|
| Sprache | englisch |
| Maße | 153 x 223 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Graphentheorie |
| ISBN-10 | 0-201-69467-0 / 0201694670 |
| ISBN-13 | 978-0-201-69467-3 / 9780201694673 |
| Zustand | Neuware |
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