Frank Simon

• The focus of this thesis lies on the application of enumerative combinatorics to the partition lattice n. Some ideas beyond enumerative combinatorics are used to examine the lattice properties of n. The combinatorial aspects involve the counting of chains in the partition lattice with the associated exponential generating functions and a new derivation of the Möbius function in n. Finally different representations of some simple sums ranging over intervals in the partition lattice are discussed.