Counting Restricted Integer Partitions

The first chapter examines pb(n), the number of partitions of n into powers of b, along with a family of identities which can be deduced by iterating a recurrence satisfied by pb(n) in a suitable way. These identities can then be used to calculate pb( n) for large values of n..;The second chapter restricts these types of partitions even further, limiting the multiplicity of each part. Its object of study is p b,d(n), that is, the number of partitions of n into powers of b repeating each power at most d times. The methods of the first chapter are applied, and the self-similarity of these sequences is discussed in detail.;The third chapter focuses on pA,M( n), the number of partitions of n with parts in A and multiplicities in M. A construction of Alon which produces infinite sets A and M so that pA,M(n) = 1 is generalized so that A can be chosen to be a subset of powers of a given base.