ABSTRACT
Incidence algebras developed as the natural setting for generalizations of the Möbius inversion formula of number theory. It would then be expected that the generalized inversion formulas would have important combinatorial implications. This chapter begins with Rota’s formula because of its significance, and presents several properties satisfied by the Mobius function. It presents several applications of Mobius inversion, each of which is of some algebraic interest. The chapter presents Rota’s result using the terminology of filters and ideals, and presents a discussion of filters and ideals on a lattice. The Mobius inversion theorem highlights the importance of the Mobius function in the incidence algebra.
