@article {1208.20057,
	title = {The cardinal and the idempotent number of various monoids of transformations on a finite chain.},
	journal = {Bulletin of the Malaysian Mathematical Sciences Society},
	volume = {34},
	number = {1},
	year = {2011},
	pages = {79-85},
	abstract = {<p>Summary: We consider various classes of monoids of transformations on a finite chain, in particular of transformations that preserve or reverse either the order or the orientation. Being finite monoids we are naturally interested in computing both their cardinals and their idempotent numbers. Fibonacci and Lucas numbers play an essential role in the last computations.</p>
},
	keywords = {monoids of transformations, numbers of idempotents, numbers of order-preserving transformations, numbers of orientation preserving transformations},
	author = {Fernandes, V{\'\i}tor H. and Gomes, Gracinda M. S. and Jesus, Manuel M.}
}
