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Combinatorics

By Fred S. Roberts (auth.), Fred Roberts (eds.)

ISBN-10: 1468463810

ISBN-13: 9781468463811

ISBN-10: 1468463837

ISBN-13: 9781468463835

This IMA quantity in arithmetic and its purposes purposes of Combinatorics and Graph conception to the organic and Social Sciences is predicated at the complaints of a workshop which was once an essential component of the 1987-88 IMA application on utilized COMBINATORICS. we're thankful to the medical Committee: Victor Klee (Chairman), Daniel Kleitman, Dijen Ray-Chaudhuri and Dennis Stanton for making plans and imposing a thrilling and stimulating yr­ lengthy application. We particularly thank the Workshop Organizers, Joel Cohen and Fred Roberts, for organizing a workshop which introduced jointly some of the significant figures in a number of examine fields attached with the appliance of combinatorial rules to the social and organic sciences. A vner Friedman Willard Miller functions OF COMBINATORICS AND GRAPH conception TO THE organic AND SOCIAL SCIENCES: SEVEN primary principles FRED S. RoBERTS* summary. To set the degree for the opposite papers during this quantity, seven basic options which come up within the purposes of combinatorics and graph concept within the organic and social sciences are defined. those rules are: RNA chains as "words" in a four letter alphabet; period graphs; festival graphs or area of interest overlap graphs; qualitative balance; balanced signed graphs; social welfare features; and semiorders. for every suggestion, a few easy effects are awarded, a few contemporary effects are given, and a few open difficulties are mentioned.

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17 (1987), pp. 269-280. , Foundational Aspects of Theories of Measurement, J. Symb. Logic, 23 (1958), pp. 113-128. , The Double Competition Number of Some Triangle-free Graphs, mimeographed, Department of Mathematics, Mount Saint Vincent University, Halifax, Nova Scotia, Canada (1988). S. ) , Applications of COIl)binatorics and Graph Theory in the Biological and Social Sciences, IMA Volumes in Mathematics and its Applications, Springer-Verlag, New York, 1989. , Collective Choice and Social Welfare, Holden-Day, San Francisco, 1970.

We propose some considerations about computability in Social Choice theory and review some recent NP-completeness results. The second deals with a formal theory of aggregation which involves, rather than the structures of individual and social preferences, structures on sets of preferences. The IMA meeting was devoted to applications of combinatorics and graph theory to Biology and Social Sciences. So, and that is the third point, we will point out connections between Social Welfare and the so-called Consensus Problem in Taxonomy and/or in Evolution Theory, each time we will have an opportunity to do this (for more details on this last point, see Barthelemy, Leclerc and Monjardet, 1986).

Mathematical Methods in the Social Sciences, Stanford University Press, Stanford, CA" 1960, pp. 16-26. , Computers in Molecular Biology: Current Applications and Emerging Trends, Science, 240 (1988), pp. 47-52. , Threshold Representations of Multiple Semiorders, SIAM J. Alg. & Discr. , 8 (1987), pp. 77-84. , A Characterization of Competition Graphs, Discr. App!. , 6 (1983), pp. 315-317. S. ), Applications of Combinatorics and Graph Theory in the Biological and Social Sciences, IMA Volumes in Mathematics and its Applications, Springer-Verlag, New York, 1989.

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Applications of Combinatorics and Graph Theory to the Biological and Social Sciences by Fred S. Roberts (auth.), Fred Roberts (eds.)


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