Principles of Combinatorics
Published on 14. May 2014
189 pages
978-0-08-095581-0 (ISBN)
Description
Berge's Principles of Combinatorics is now an acknowledged classic work of the field. Complementary to his previous books, Berge's introduction deals largely with enumeration. The choice of topics is balanced, the presentation elegant, and the text can be followed by anyone with an interest in the subject with only a little algebra required as a background. Some topics were here described for the first time, including Robinston-Shensted theorum, the Eden-Schutzenberger theorum, and facts connecting Young diagrams, trees, and the symmetric group.
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Series
Language
English
Place of publication
San Diego
United States
ISBN-13
978-0-08-095581-0 (9780080955810)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Claude Berge
Principles of Combinatorics
Book
01/1971
Academic Press
€46.51
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Content
- 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 A
- 6. 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 Lattice
- References
- 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 Bruijn
- 4. Computing the Cycle Index
- References
- Index
