Some Combinatorial Aspects of Lattice of Residual Mappings
Mohand Amokrane Yazi · HAL (Le Centre pour la Communication Scientifique Directe) · 2011
We have developed and extended the study of some combinatorial aspects of lattice of isotone mappings to the case of lattice of residual mappings between two finite lattices of combinatorial structure. The algebraic characterization of residual mapping allows us to study the covering relation in the lattice of ultrametrics and to give a way for describing the lattice of closure operators on a finite chain. In the final point, we give a necessary condition for a class of couples of closures and anti-closures to be a Galois connection on finite distributive lattice.