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Notes on Introductory Combinatorics

  • Book
  • © 1983

Overview

Authors:
  1. George Pólya

    1. Department of Mathematics, Stanford University, Stanford, USA

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  2. Robert E. Tarjan

    1. Bell Laboratories, Murray Hill, USA

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    You can also search for this author in PubMed   Google Scholar

  3. Donald R. Woods

    1. Xerox Corporation, Palo Alto, USA

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Part of the book series: Progress in Computer Science and Applied Logic (PCS, volume 4)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Introduction

    • George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 1-1

  3. Combinations and Permutations

    • George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 2-10

  4. Generating Functions

    • George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 11-31

  5. Principle of Inclusion and Exclusion

    • George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 32-40

  6. Stirling Numbers

    • George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 41-54

  7. Pólya’s Theory of Counting

    • George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 55-85

  8. Outlook

    • George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 86-94

  9. Midterm Examination

    • George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 95-115

  10. Ramsey Theory

    • George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 116-127

  11. Matchings (Stable Marriages)

    • George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 128-134

  12. Matchings (Maximum Matchings)

    • George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 135-151

  13. Network Flow

    • George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 152-156

  14. Hamiltonian and Eulerian Paths

    • George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 157-168

  15. Planarity and the Four-Color Theorem

    • George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 169-181

  16. Final Examination

    • George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 182-190

  17. Bibliography

    • George Pólya, Robert E. Tarjan, Donald R. Woods
    Pages 191-191

  18. Back Matter

    Pages 192-193
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Keywords

About this book

In the winter of 1978, Professor George P61ya and I jointly taught Stanford University's introductory combinatorics course. This was a great opportunity for me, as I had known of Professor P61ya since having read his classic book, How to Solve It, as a teenager. Working with P6lya, who ·was over ninety years old at the time, was every bit as rewarding as I had hoped it would be. His creativity, intelligence, warmth and generosity of spirit, and wonderful gift for teaching continue to be an inspiration to me. Combinatorics is one of the branches of mathematics that play a crucial role in computer sCience, since digital computers manipulate discrete, finite objects. Combinatorics impinges on computing in two ways. First, the properties of graphs and other combinatorial objects lead directly to algorithms for solving graph-theoretic problems, which have widespread application in non-numerical as well as in numerical computing. Second, combinatorial methods provide many analytical tools that can be used for determining the worst-case and expected performance of computer algorithms. A knowledge of combinatorics will serve the computer scientist well. Combinatorics can be classified into three types: enumerative, eXistential, and constructive. Enumerative combinatorics deals with the counting of combinatorial objects. Existential combinatorics studies the existence or nonexistence of combinatorial configurations.

Authors and Affiliations

  • Department of Mathematics, Stanford University, Stanford, USA

    George Pólya

  • Bell Laboratories, Murray Hill, USA

    Robert E. Tarjan

  • Xerox Corporation, Palo Alto, USA

    Donald R. Woods

Bibliographic Information

  • Book Title: Notes on Introductory Combinatorics

  • Authors: George Pólya, Robert E. Tarjan, Donald R. Woods

  • Series Title: Progress in Computer Science and Applied Logic

  • DOI: https://doi.org/10.1007/978-1-4757-1101-1

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1983

  • Softcover ISBN: 978-0-8176-3170-3Published: 01 January 1990

  • eBook ISBN: 978-1-4757-1101-1Published: 27 November 2013

  • Series ISSN: 2297-0576

  • Series E-ISSN: 2297-0584

  • Edition Number: 1

  • Number of Pages: IX, 193

  • Number of Illustrations: 3 b/w illustrations

  • Additional Information: Softcover reprint of the original hardcover edition (ISBN 0-8176-3132-2)

  • Topics: Science, Humanities and Social Sciences, multidisciplinary

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