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Applications of the Probabilistic Method to Partially Ordered Sets

In: The Mathematics of Paul Erdős II

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  • William T. Trotter

    (Department of Mathematics
    Georgia Institute of Technology, School of Mathematics)

Abstract

Summary There are two central themes to research involving applications of probabilistic methods to partially ordered sets. The first of these can be described as the study of random partially ordered sets. Among the specific models which have been studied are: random labelled posets; random t-dimensional posets; and the transitive closure of random graphs. A second theme concentrates on the adaptation of random methods so as to be applicable to general partially ordered sets. In this paper, we concentrate on the second theme. Among the topics we discuss are fibers and co-fibers; the dimension of subposets of the subset lattice; the dimension of posets of bounded degree; and fractional dimension. This last topic leads to a discussion of Ramsey theoretic questions for probability spaces.

Suggested Citation

  • William T. Trotter, 2013. "Applications of the Probabilistic Method to Partially Ordered Sets," Springer Books, in: Ronald L. Graham & Jaroslav Nešetřil & Steve Butler (ed.), The Mathematics of Paul Erdős II, edition 2, pages 313-329, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-7254-4_20
    DOI: 10.1007/978-1-4614-7254-4_20
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