The purpose of this paper is to show that the lattice Sn of permutations on a n-element set is bounded. This result strengthens the semi-distributive nature of the lattice Sn. To prove this property, we use a characterization of the class of bounded lattices in terms of arrows relations defined...

The purpose of this paper is to provide a characterization result for the canonical basis of an arbitrary closure operator. This theorem strengthens the result of Burosch, Demetrovics and Katona, who propose in [1] a characterization of the generating system of a closure operator defined by the...

We have recalled that all interval doubling schemes of a bounded lattice L are in bijection with all different ways to conduct L starting from the two-element lattice by doublings of convex sets.

We present a survey of properties of the lattice of closure systems (families of subsets of a set S containing S and closed by set intersection) on a finite set S with proofs of the more significant results. In particular, we prove that this lattice is atomistic and lower bounded and that there...