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The bulletin of mathematical biophysics

, Volume 16, Issue 2, pp 131–140 | Cite as

Structures of dominance relations

  • Robert L. Davis
Article

Abstract

Dominance relations and theirstructures have been studied in the context of animal sociology (Rapoport, 1949a, b; Landau, 1951a, b), and occur in many other theoretical models of the social and biological sciences. When Rapoport and Landau wrote, there was no method known for determining the number of dominance structures which could be defined on a set ofn elements, forn>4. The answer to this question can be important in certain further investigations of the structural properties of dominance. Using a general method developed elsewhere (Davis, 1953), this paper derives a formula to answer the question for anyn, and gives an application of the method to treat a case not previously analyzed.

Keywords

Conjugate Class Symmetric Group Dominance Relation Biophysics Volume Structure Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literature

  1. Davis, R. L. 1953. “The Number of Structures of Finite Relations.”Proc. Amer. Math. Soc.,4, 486–95.MATHMathSciNetCrossRefGoogle Scholar
  2. Landau, H. G. 1951a. “On Dominance Relations and the Structure of Animal Societies: I.”Bull. Math. Biophysics,13, 1–19.CrossRefGoogle Scholar
  3. Landau, H. G. 1951b. “On Dominance Relations and the Structure of Animal Societies: II.” —Ibid., 245–62.MATHCrossRefGoogle Scholar
  4. — 1953. “On Dominance Relations and the Structure of Animal Societies: III.” —Ibid., 143–48.CrossRefGoogle Scholar
  5. Rapoport, A. 1949a. “Outline of a Probabilistic Approach to Animal Sociology: I.”Bull. Math. Biophysics,11, 183–96.CrossRefGoogle Scholar
  6. — 1949a. “Outline of a Probabilistic Approach to Animal Sociology: II.” —Ibid.,11, 273–82.CrossRefGoogle Scholar
  7. Russell, B. 1919.Introduction to Mathematical Philosophy. London: G. Allen and Unwin.Google Scholar

Copyright information

© University of Chicago 1954

Authors and Affiliations

  • Robert L. Davis
    • 1
  1. 1.University of MichiganMichiganUSA

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