%0 Journal Article
%J Bulletin of the Malaysian Mathematical Sciences Society
%D 2011
%T The cardinal and the idempotent number of various monoids of transformations on a finite chain.
%A Fernandes, VĂtor H.
%A Gomes, Gracinda M. S.
%A Jesus, Manuel M.
%K monoids of transformations
%K numbers of idempotents
%K numbers of order-preserving transformations
%K numbers of orientation preserving transformations
%N 2
%P 79-85
%V 34
%X 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.