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Incidence posets of trees in posets of large dimension

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Abstract

In this paper, we investigate substructures of partially ordered sets which must be present whenever the dimension is large. We show that for eachn⩾1, ifT is a tree onn vertices and ifP is any poset having dimension at least 4n 6, then eitherP or its dual contains the incidence poset ofT as a suborder.

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Authors and Affiliations

  1. Department of Mathematics, London School of Economics, Houghton Street, WC2A 2AE, London, UK

    Graham R. Brightwell

  2. Bell Communications Research, 445 South Street 2L-367, 07962, Morristown, NJ, USA

    William T. Trotter

  3. Department of Mathematics, Arizona State University, 85287, Tempe, AZ, USA

    William T. Trotter

Authors
  1. Graham R. Brightwell
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  2. William T. Trotter
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Communicated by D. Kelly

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Brightwell, G.R., Trotter, W.T. Incidence posets of trees in posets of large dimension. Order 11, 159–167 (1994). https://doi.org/10.1007/BF01108600

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  • DOI: https://doi.org/10.1007/BF01108600

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