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

  • Conference proceedings
  • © 1989

Overview

Editors:
  1. Fred Roberts

    1. Department of Mathematics, Rutgers University, New Brunswick, USA

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

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Table of contents (15 papers)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Applications of Combinatorics and Graph Theory to the Biological and Social Sciences: Seven Fundamental Ideas

    • Fred S. Roberts
    Pages 1-37

  3. Social Welfare and Aggregation Procedures: Combinatorial and Algorithmic Aspects

    • Jean-Pierre Barthélemy
    Pages 39-73

  4. Consecutive One’s Properties for Matrices and Graphs Including Variable Diagonal Entries

    • Margaret B. Cozzens, N. V. R. Mahadev
    Pages 75-94

  5. Probabilistic Knowledge Spaces: A Review

    • Jean-Claude Falmagne
    Pages 95-101

  6. Uniqueness in Finite Measurement

    • Peter C. Fishburn, Fred S. Roberts
    Pages 103-137

  7. Conceptual Scaling

    • Bernhard Ganter, Rudolf Wille
    Pages 139-167

  8. The Micro-Macro Connection: Exact Structure and Process

    • Eugene C. Johnsen
    Pages 169-201

  9. Sign-Patterns and Stability

    • Victor Klee
    Pages 203-219

  10. Food Webs, Competition Graphs, Competition-Common Enemy Graphs, and Niche Graphs

    • J. Richard Lundgren
    Pages 221-243

  11. Qualitatively Stable Matrices and Convergent Matrices

    • John S. Maybee
    Pages 245-258

  12. Tree Structures in Immunology

    • J. K. Percus
    Pages 259-276

  13. Meaningless Statements, Matching Experiments, and Colored Digraphs

    • Fred S. Roberts
    Pages 277-294

  14. Combinatorial Aspects of Enzyme Kinetics

    • Peter H. Sellers
    Pages 295-314

  15. Spatial Models of Power and Voting Outcomes

    • Philip D. Straffin Jr.
    Pages 315-335

  16. Some Mathematics for DNA Restriction Mapping

    • Michael S. Waterman
    Pages 337-345
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Keywords

About this book

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.

Editors and Affiliations

  • Department of Mathematics, Rutgers University, New Brunswick, USA

    Fred Roberts

Bibliographic Information

  • Book Title: Applications of Combinatorics and Graph Theory to the Biological and Social Sciences

  • Editors: Fred Roberts

  • Series Title: The IMA Volumes in Mathematics and its Applications

  • DOI: https://doi.org/10.1007/978-1-4684-6381-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1989

  • Softcover ISBN: 978-1-4684-6383-5Published: 25 February 2012

  • eBook ISBN: 978-1-4684-6381-1Published: 06 December 2012

  • Series ISSN: 0940-6573

  • Series E-ISSN: 2198-3224

  • Edition Number: 1

  • Number of Pages: IX, 345

  • Topics: Mathematical and Computational Biology, Combinatorics

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