Principles of combinatorics
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| Format: | eBook |
| Language: | English |
| Published: |
New York
Academic Press
1971, 1971
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| Series: | Mathematics in science and engineering
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| Subjects: | |
| Online Access: | |
| Collection: | Elsevier eBook collection Mathematics - Collection details see MPG.ReNa |
Table of Contents:
- Includes bibliographical references and index
- Front Cover; Principles of Combinatorics; Copyright Page; Contents; Foreword; What Is Combinatorics?; First Aspect: Study of a Known Configuration; Second Aspect : Investigation of an Unknown Configuration; Third Aspect : Counting Configurations; Fourth Aspect : Approximate Counting of Configurations; Fifth Aspect : Enumeration of Configurations; Sixth Aspect: Optimization; References; Chapter 1. The Elemientary Counting Functions; 1. Mappings of Finite Sets; 2. The Cardinality of the Cartesian Product A x X; 3. Number of Subsets of a Finite Set A; 4. Numbers mn or Mappings of X into A
- 5. Numbers [M]n, or Injections of X into A6. Numbers [M]n; 7. Numbers [m]n/n!, or Increasing Mappings of X Into A; 8. Binomial Numbers; 9. Multinomial Numbers(n n1,n2, ... np); 10. Stirling Numbers Snm, or Partitions of n Objects into m Classes; 11. Bell Exponential Number Bn, or the Number of Partitions of n Objects; References; Chapter 2. Partition Problems; 1. Pnm, or the Number of Partitions of Integer n into m Parts; 2. Pn, h, or the Number of Partitions of the Integer n Having h as the Smallest Part; 3. Counting the Standard Tableaus Associated with a Partition of n
- 4. Standard Tableaus and Young's LatticeReferences; Chapter 3. Inversion Formulas and Their Applications; 1. Differential Operator Associated with a Family of Polynomials; 2. The Möbius Function; 3. Sieve Formulas; 4. Distributions; 5. Counting Trees; References; Chapter 4. Permutation Groups; 1. Introduction; 2. Cycles of a Permutation; 3. Orbits of a Permutation Group; 4. Parity of a Permutation; 5. Decomposition Problems; References; Chapter 5. Pólya's Theorem; 1. Counting Schemata Relative to a Group of Permutations of Objects; 2. Counting Schemata Relative to an Arbitrary Group
- 3. A Theorem of de Bruijn4. Computing the Cycle Index; References; Index