Whitney numbers are combinatorial invariants of ranked partially ordered sets. Whitney numbers of the second kind count elements at each rank, whereas Whitney numbers of the first kind are obtained by summing the values of the Möbius function over elements of a fixed rank.
The thesis develops the required framework of incidence algebras, the zeta function, the Möbius function and Möbius inversion. The Möbius function is computed explicitly for chains, divisor lattices, partition lattices and lattices of subspaces over finite fields. These computations yield closed formulas for the corresponding Whitney numbers. In particular, the Whitney numbers of partition lattices are identified, up to the usual sign and reversal of indices, with Stirling numbers of the first and second kind.
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