@article {15230,
	title = {Partial Automorphisms and Injective Partial Endomorphisms of a Finite Undirected Path},
	journal = {Semigroup Forum},
	volume = {103},
	year = {2021},
	pages = {87-105},
	abstract = {<p>In this paper, we study partial automorphisms and, more generally, injective partial endomorphisms of a finite undirected path from Semigroup Theory perspective. Our main objective is to give formulas for the ranks of the monoids IEnd(P_n) and PAut(P_n) of all injective partial endomorphisms and of all partial automorphisms of the undirected path P_n with n vertices. We also describe Green{\textquoteright}s relations of PAut(P_n) and IEnd(P_n) and calculate their cardinals.</p>
},
	url = {https://link.springer.com/article/10.1007/s00233-021-10193-y},
	author = {Dimitrova, I. and Fernandes, V{\'\i}tor H. and Koppitz, J. and T.M. Quinteiro}
}
