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.
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Literature
Davis, R. L. 1953. “The Number of Structures of Finite Relations.”Proc. Amer. Math. Soc.,4, 486–95.
Landau, H. G. 1951a. “On Dominance Relations and the Structure of Animal Societies: I.”Bull. Math. Biophysics,13, 1–19.
Landau, H. G. 1951b. “On Dominance Relations and the Structure of Animal Societies: II.” —Ibid., 245–62.
— 1953. “On Dominance Relations and the Structure of Animal Societies: III.” —Ibid., 143–48.
Rapoport, A. 1949a. “Outline of a Probabilistic Approach to Animal Sociology: I.”Bull. Math. Biophysics,11, 183–96.
— 1949a. “Outline of a Probabilistic Approach to Animal Sociology: II.” —Ibid.,11, 273–82.
Russell, B. 1919.Introduction to Mathematical Philosophy. London: G. Allen and Unwin.
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This research was begun while the author was working under a Ford Foundation Behavioral Sciences grant to the University of Michigan.
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Davis, R.L. Structures of dominance relations. Bulletin of Mathematical Biophysics 16, 131–140 (1954). https://doi.org/10.1007/BF02478368
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DOI: https://doi.org/10.1007/BF02478368