Geodesic
The cardinalities of semigroups of isotonic transformations of reflexive graphs
Matematičeskie zametki, Tome 16 (1974) no. 2, pp. 317-323

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We prove that the semigroup of all isotonic transformations of an infinite partially ordered set is nondenumerable. We construct an example of a reflexive graph, the semigroup of all isotonic transformations of which is denumerable. 
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     author = {Yu. M. Vazhenin},
     title = {The cardinalities of semigroups of isotonic transformations of reflexive graphs},
     journal = {Matemati\v{c}eskie zametki},
     pages = {317--323},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_2_a15/}
}
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Yu. M. Vazhenin. The cardinalities of semigroups of isotonic transformations of reflexive graphs. Matematičeskie zametki, Tome 16 (1974) no. 2, pp. 317-323. http://geodesic.mathdoc.fr/item/MZM_1974_16_2_a15/