Geodesic
Presentations for subsemigroups of $PD_n$
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 2, pp. 417-426.

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Let $[n]=\{1,\ldots ,n\}$ be an $n$-chain. We give presentations for the following transformation semigroups: the semigroup of full order-decreasing mappings of $[n]$, the semigroup of partial one-to-one order-decreasing mappings of $[n]$, the semigroup of full order-preserving and order-decreasing mappings of $[n]$, the semigroup of partial one-to-one order-preserving and order-decreasing mappings of $[n]$, and the semigroup of partial order-preserving and order-decreasing mappings of $[n]$.
DOI : 10.21136/CMJ.2018.0343-17
Classification : 20M20, 20M30
Keywords: presentation; order-decreasing mapping; order-preserving mapping; transformation semigroups 
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     title = {Presentations for subsemigroups of $PD_n$},
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Umar, Abdullahi. Presentations for subsemigroups of $PD_n$. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 2, pp. 417-426. doi : 10.21136/CMJ.2018.0343-17. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0343-17/

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