@article {15880,
	title = {On the Rank of Monoids of Endomorphisms of a Finite Directed Path},
	journal = {Asian-European Journal of Mathematics (DOI 10.1142/S1793557123500699; Online 28 Oct 2022)},
	volume = {16},
	year = {2023},
	pages = {2350069 (13 pages)},
	abstract = {<p>In this paper we consider endomorphisms of a finite directed path from monoid generators perspective. Our main aim is to determine the rank of the monoid wEndP_n of all weak endomorphisms of a directed path with n vertices, which is a submonoid of the widely studied monoid O_n of all order-preserving transformations of a n-chain. Also, we describe the regular elements of wEndP_n and calculate its size and number of idempotents.</p>
},
	url = {https://doi.org/10.1142/S1793557123500699},
	author = {Fernandes, V{\'\i}tor H. and Paulista, T{\^a}nia}
}
