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Enumeration of order preserving maps

โœ Scribed by Dwight Duffus; Vojtech Rodl; Bill Sands; Robert Woodrow

Publisher
Springer Netherlands
Year
1992
Tongue
English
Weight
757 KB
Volume
9
Category
Article
ISSN
0167-8094

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โœฆ Synopsis

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'"" order preserving maps (and 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.

Mathematics

Subject Classification (1991). 06A06.

๐Ÿ“œ SIMILAR VOLUMES

Recognition of order-preserving maps
Recognition of order-preserving maps
โœ Konrad Engel ๐Ÿ“‚ Article ๐Ÿ“… 1985 ๐Ÿ› Springer Netherlands ๐ŸŒ English โš– 384 KB
The number of order-preserving maps of f
The number of order-preserving maps of fences and crowns
โœ J. D. Currie; T. I. Visentin ๐Ÿ“‚ Article ๐Ÿ“… 1991 ๐Ÿ› Springer Netherlands ๐ŸŒ English โš– 460 KB

We perform an exact enumeration of the order-preserving maps of fences (zig-zags) and crowns (cycles). From this we derive asymptotic results.