Title of article :
The Cardinal and the Idempotent Number of Various Monoids of Transformations on a Finite Chain
Author/Authors :
Fernandes, Vitor H. Universidade de Lisboa - Centro de Algebra, Portugal , Fernandes, Vitor H. Universidade Nova de Lisboa - Faculdade de Ciencias e Tecnologia - Departamento de Matematica, Portugal , Gomes, Gracinda M. S. Universidade de Lisboa - Centro de Algebra, Faculdade de Ciencias - Departamento de Matematica, Portugal , Jesus, Manuel M. Universidade de Lisboa - Centro de Algebra, Faculdade de Ciencias e Tecnologia - Departamento de Matematica, Portugal
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.
Keywords :
Monoid , transformation , order , preserving , orientation , preserving
Journal title :
Bulletin of the Malaysian Mathematical Sciences Society
Journal title :
Bulletin of the Malaysian Mathematical Sciences Society
