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Applications of Combinatorics and Graph Theory to the Biological and Social Sciences

  • Fred Roberts

Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 17)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Jean-Claude Falmagne
    Pages 95-101
  3. Peter C. Fishburn, Fred S. Roberts
    Pages 103-137
  4. Bernhard Ganter, Rudolf Wille
    Pages 139-167
  5. Victor Klee
    Pages 203-219
  6. J. K. Percus
    Pages 259-276
  7. Peter H. Sellers
    Pages 295-314
  8. Philip D. Straffin Jr.
    Pages 315-335
  9. Michael S. Waterman
    Pages 337-345

About these proceedings

Introduction

This IMA Volume in Mathematics and its Applications Applications of Combinatorics and Graph Theory to the Biological and Social Sciences is based on the proceedings of a workshop which was an integral part of the 1987-88 IMA program on APPLIED COMBINATORICS. We are grateful to the Scientific Committee: Victor Klee (Chairman), Daniel Kleitman, Dijen Ray-Chaudhuri and Dennis Stanton for planning and implementing an exciting and stimulating year­ long program. We especially thank the Workshop Organizers, Joel Cohen and Fred Roberts, for organizing a workshop which brought together many of the major figures in a variety of research fields connected with the application of combinatorial ideas to the social and biological sciences. A vner Friedman Willard Miller APPLICATIONS OF COMBINATORICS AND GRAPH THEORY TO THE BIOLOGICAL AND SOCIAL SCIENCES: SEVEN FUNDAMENTAL IDEAS FRED S. RoBERTS* Abstract. To set the stage for the other papers in this volume, seven fundamental concepts which arise in the applications of combinatorics and graph theory in the biological and social sciences are described. These ideas are: RNA chains as "words" in a 4 letter alphabet; interval graphs; competition graphs or niche overlap graphs; qualitative stability; balanced signed graphs; social welfare functions; and semiorders. For each idea, some basic results are presented, some recent results are given, and some open problems are mentioned.

Keywords

Combinatorics Matching algorithms genetics graph theory graphs kinetics mapping mathematics

Editors and affiliations

  • Fred Roberts
    • 1
  1. 1.Department of MathematicsRutgers UniversityNew BrunswickUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-6381-1
  • Copyright Information Springer-Verlag New York 1989
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4684-6383-5
  • Online ISBN 978-1-4684-6381-1
  • Series Print ISSN 0940-6573
  • Buy this book on publisher's site
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