Order

, Volume 9, Issue 1, pp 15–29 | Cite as

Enumeration of order preserving maps

  • Dwight Duffus
  • Vojtech Rodl
  • Bill Sands
  • Robert Woodrow
Article

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.

Mathematics Subject Classification (1991)

06A06 

Key words

(Partially) ordered set order preserving map enumeration stochastic process martingale 

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Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • Dwight Duffus
    • 1
  • Vojtech Rodl
    • 1
  • Bill Sands
    • 2
  • Robert Woodrow
    • 2
  1. 1.Mathematics and Computer ScienceEmory UniversityAtlantaUSA
  2. 2.Mathematics and StatisticsThe University of CalgaryCalgaryCanada

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