@article {16548,
	title = {On the cyclic inverse monoid on a finite set},
	journal = {Asian-European Journal of Mathematics (DOI 10.1142/S1793557124500177; Online 6 March 2024)},
	volume = {17},
	year = {2024},
	pages = {2450017 (16 pages)},
	abstract = {<p>In this paper we study the cyclic inverse monoid CI_n on a set Ω_n with n elements, i.e. the inverse submonoid of the symmetric inverse monoid on Ω_n consisting of all restrictions of the elements of a cyclic subgroup of order n acting cyclically on Ω_n. We show that CI_n has rank 2 (for n⩾2) and n.2^n-n+1 elements. Moreover, we give presentations of CI_n on n+1 generators and (n^2+3n+4)/2 relations and on 2 generators and (n^2-n+6)/2 relations. We also consider the remarkable inverse submonoid OCI_n of CI_n constituted by all its order-preserving transformations. We show that OCI_n has rank n and 3.2^n-2n-1 elements. Furthermore, we exhibit presentations of OCI_n on n+2 generators and (n^2+3n+8)/2 relations and on n generators and (n^2+3n)/2 relations.</p>
},
	url = {https://doi.org/10.1142/S1793557124500177},
	author = {Fernandes, V{\'\i}tor H.}
}
