ABSTRACT
This chapter begins with a discussion of the generalized distributive law and its consequences, which include the multinomial and binomial theorems. We then study algebraic and combinatorial proofs of identities involving binomial coefficients, factorials, summations, etc. We also introduce recursions, which provide ways to enumerate classes of combinatorial objects whose cardinalities are not given by closed formulas. We use recursions to obtain information about more intricate combinatorial objects including set partitions, integer partitions, equivalence relations, surjections, and lattice paths.
