Constructive Combinatorics
The notes that eventually became this book were written between 1977 and 1985 for the course called Constructive Combinatorics at the University of Minnesota. This is a one-quarter (10 week) course for upper level undergraduate students. The class usually consists of mathematics and computer science...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1986, 1986
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| Edition: | 1st ed. 1986 |
| Series: | Undergraduate Texts in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Listing Basic Combinatorial Objects
- 1.1 Permutations
- 1.2 Subsets
- 1.3 Integer Partitions
- 1.4 Product Spaces
- 1.5 Set Partitions
- Notes
- Exercises
- 2 Partially Ordered Sets
- 2.1 Six Posets
- 2.2 Matching the Boolean Algebra
- 2.3 The Littlewood-Offord Problem
- 2.4 Extremal Set Theory
- Notes
- Exercises
- 3 Bijections
- 3.1 The Catalan Family
- 3.2 The Prüfer Correspondence
- 3.3 Partitions
- 3.4 Permutations
- 3.5 Tableaux
- 3.6 The Schensted Correspondence
- 3.7 Properties of the Schensted Correspondence
- Notes
- Exercises
- 4 Involutions
- 4.1 The Euler Pentagonal Number Theorem
- 4.2 Vandermonde’s Determinant
- 4.3 The Cayley-Hamilton Theorem
- 4.4 The Matrix-Tree Theorem
- 4.5 Lattice Paths
- 4.6 The Involution Principle
- Notes
- Exercises
- A.1 Permutations
- A.2 Subsets
- A.3 Set Partitions
- A.4 Integer Partitions
- A.5 Product Spaces
- A.6 Match to First Available
- A.7 The Schensted Correspondence
- A.8 The Prüfer Correspondence
- A.9 The Involution Principle