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Independence Theory in Combinatorics

An Introductory Account with Applications to Graphs and Transversals

  • Victor Bryant
  • Hazel Perfect

Table of contents

  1. Front Matter
    Pages i-xii
  2. Victor Bryant, Hazel Perfect
    Pages 1-11
  3. Victor Bryant, Hazel Perfect
    Pages 13-40
  4. Victor Bryant, Hazel Perfect
    Pages 41-63
  5. Victor Bryant, Hazel Perfect
    Pages 65-99
  6. Victor Bryant, Hazel Perfect
    Pages 101-116
  7. Back Matter
    Pages 117-144

About this book

Introduction

Combinatorics may very loosely be described as that branch of mathematics which is concerned with the problems of arranging objects in accordance with various imposed constraints. It covers a wide range of ideas and because of its fundamental nature it has applications throughout mathematics. Among the well-established areas of combinatorics may now be included the studies of graphs and networks, block designs, games, transversals, and enumeration problem s concerning permutations and combinations, from which the subject earned its title, as weil as the theory of independence spaces (or matroids). Along this broad front,various central themes link together the very diverse ideas. The theme which we introduce in this book is that of the abstract concept of independence. Here the reason for the abstraction is to unify; and, as we sh all see, this unification pays off handsomely with applications and illuminating sidelights in a wide variety of combinatorial situations. The study of combinatorics in general, and independence theory in particular, accounts for a considerable amount of space in the mathematical journais. For the most part, however, the books on abstract independence so far written are at an advanced level, ·whereas the purpose of our short book is to provide an elementary in­ troduction to the subject.

Keywords

Abstraction Combinatorics Permutation constraint design functions games graph graphs mathematics matroid mutation object themes theorem

Authors and affiliations

  • Victor Bryant
    • 1
  • Hazel Perfect
    • 1
  1. 1.Department of Pure MathematicsUniversity of SheffieldUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-009-5900-2
  • Copyright Information Springer Science+Business Media B.V. 1980
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-412-22430-0
  • Online ISBN 978-94-009-5900-2
  • Buy this book on publisher's site
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