Georgia Institute of Technology College of Sciences

I will talk about the problem of computing the number of integer partitions into parts lying in some integer sequence. We prove that for certain classes of infinite sequences the number of associated partitions of an input N can be computed in time polynomial in its bit size, log N. Special cases include binary partitions (i.e. partitions into powers of two) that have a key connection with Cayley compositions and polytopes. Some questions related to algebraic differential equations for partition sequences will also be discussed. (This is joint work with Igor Pak.)