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Enumeration of order preserving maps

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Abstract

Three results are obtained concerning the number of order preserving maps of an n-element partially ordered set to itself. We show that any such ordered set has at least 22n/3 order preserving maps (and 22 in the case of length one). Precise asymptotic estimates for the numbers of self-maps of crowns and fences are also obtained. In addition, lower bounds for many other infinite families are found and several precise problems are formulated.

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Authors and Affiliations

  1. Mathematics and Computer Science, Emory University, 30322, Atlanta, GA, USA

    Dwight Duffus & Vojtech Rodl

  2. Mathematics and Statistics, The University of Calgary, T2N 1N4, Calgary, Alberta, Canada

    Bill Sands & Robert Woodrow

Authors
  1. Dwight Duffus
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  2. Vojtech Rodl
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  3. Bill Sands
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  4. Robert Woodrow
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Additional information

Communicated by N. Zaguia

Supported by ONR Contract N00014-85-K-0769.

Supported by NSF Grant DMS-9011850.

Supported by NSERC Grants 69-3378 and 69-0259.

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Duffus, D., Rodl, V., Sands, B. et al. Enumeration of order preserving maps. Order 9, 15–29 (1992). https://doi.org/10.1007/BF00419036

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  • DOI: https://doi.org/10.1007/BF00419036

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