, Volume 9, Issue 1, pp 15-29

Enumeration of order preserving maps

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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 2 2n/3 order preserving maps (and 2 2 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.