Geodesic
Defining relations of semigroups of all directed transformations of an~ordered finite set
Matematičeskie zametki, Tome 3 (1968) no. 6, pp. 657-662.

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The semigroup $\mathfrak A$ of all transformations $X$ of a finite (partially) ordered set $\Omega$, such that $\alpha\le X\alpha$ for all $\alpha\in\Omega$, is considered. All possible generating sets of a $\Omega$ are elucidated. Only one of those sets is irreducible. A system of defining relations is found for that generating set. 
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     author = {E. S. Lyapin},
     title = {Defining relations of semigroups of all directed transformations of an~ordered finite set},
     journal = {Matemati\v{c}eskie zametki},
     pages = {657--662},
     publisher = {mathdoc},
     volume = {3},
     number = {6},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_3_6_a4/}
}
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E. S. Lyapin. Defining relations of semigroups of all directed transformations of an~ordered finite set. Matematičeskie zametki, Tome 3 (1968) no. 6, pp. 657-662. http://geodesic.mathdoc.fr/item/MZM_1968_3_6_a4/