Lattice of All Subsets of a Finite Set and Partition Lattice of an \(n\)-Set

Abstract

This paper uses research methods in the subspace lattices, making a deep research to the lattices of all subsets of a finite set and partition of an n-set. At first, the inclusion relations between different lattices are studied. Then, a characterization of elements contained in a given lattice is given. Finally, the characteristic polynomials of the given lattices are computed.