Incidence algebras

the long version

This unique, up-to-the-minute reference/text presents many properties of the incidence algebra of a locally finite partially ordered set X over a ring R - focusing specifically on the case when R is a commutative ring with identity and detailing various properties of the Mobius function, including classical and new applications of Mobius inversion suitable for use in combinatorics courses. Furnishing nearly 730 references, equations, and drawings and requiring no more than an introductory abstract algebra course as a prerequisite, Incidence Algebras is a vital reference for algebraists and number theorists, combinatorists, and ring theorists and a highly accessible text for upper-level undergraduate and graduate students in these disciplines.