Volume 34 • Number 1 • 2011   • The Cardinal and the Idempotent Number of Various Monoids of Transformations on a Finite Chain Vítor H. Fernandes, Gracinda M. S. Gomes and Manuel M. Jesus Abstract. In this note 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. 2010 Mathematics Subject Classification: Primary: 20M17; Secondary: 20M20, 05A10. Full text: PDF