, 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.

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.