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The convexity lattice of a poset

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Abstract

The authors investigate the lattice Co(P) of convex subsets of a general partially ordered set P. In particular, they determine the conditions under which Co(P) and Co(Q) are isomorphic; and give necessary and sufficient conditions on a lattice L so that L is isomorphic to Co(P) for some P.

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Authors and Affiliations

  1. Department of Mathematics, Harvard University, 02138, Cambridge, MA, USA

    Garrett Birkhoff

  2. Department of Mathematics and Statistics, University of Massachusetts, 01003, Amherst, MA, USA

    M. K. Bennett

Authors
  1. Garrett Birkhoff
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  2. M. K. Bennett
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Communicated by D. Kelly

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Birkhoff, G., Bennett, M.K. The convexity lattice of a poset. Order 2, 223–242 (1985). https://doi.org/10.1007/BF00333128

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  • DOI: https://doi.org/10.1007/BF00333128

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