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Combinatorial techniques

  • Book
  • © 2013

Overview

Authors:
  1. Sharad S. Sane

    1. Indian Institute of Technology, Mumbai, India

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Part of the book series: Texts and Readings in Mathematics (TRM, volume 65)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xv
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  2. Basic counting

    • Sharad S. Sane
    Pages 1-24

  3. Listing combinatorial objects

    • Sharad S. Sane
    Pages 25-37

  4. Permutations

    • Sharad S. Sane
    Pages 39-56

  5. The inclusion-exclusion principle

    • Sharad S. Sane
    Pages 57-79

  6. Basic probability

    • Sharad S. Sane
    Pages 81-104

  7. Random variables

    • Sharad S. Sane
    Pages 105-128

  8. Parity

    • Sharad S. Sane
    Pages 129-167

  9. Pigeonhole principle

    • Sharad S. Sane
    Pages 169-192

  10. Some geometry

    • Sharad S. Sane
    Pages 193-218

  11. Advanced counting numbers

    • Sharad S. Sane
    Pages 219-242

  12. Recurrence relations

    • Sharad S. Sane
    Pages 243-282

  13. Generating functions

    • Sharad S. Sane
    Pages 283-324

  14. Partition theory of integers

    • Sharad S. Sane
    Pages 325-352

  15. Group action on a set

    • Sharad S. Sane
    Pages 353-384

  16. Polya theory of enumeration

    • Sharad S. Sane
    Pages 385-420

  17. Systems of distinct representatives

    • Sharad S. Sane
    Pages 421-455

  18. Back Matter

    Pages 457-468
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About this book

This is a basic text on combinatorics that deals with all the three aspects of the discipline: tricks, techniques and theory, and attempts to blend them. The book has several distinctive features. Probability and random variables with their interconnections to permutations are discussed. The theme of parity has been specially included and it covers applications ranging from solving the Nim game to the quadratic reciprocity law. Chapters related to geometry include triangulations and Sperner's theorem, classification of regular polytopes, tilings and an introduction to the Eulcidean Ramsey theory. Material on group actions covers Sylow theory, automorphism groups and a classification of finite subgroups of orthogonal groups. All chapters have a large number of exercises with varying degrees of difficulty, ranging from material suitable for Mathematical Olympiads to research.

Authors and Affiliations

  • Indian Institute of Technology, Mumbai, India

    Sharad S. Sane

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