Geometry and complexity of O'Hara's algorithm

O'Hara's bijection is a well known bijection generalizing Glaisher's bijection between partitions into distinct and odd parts. The bijection is very natural and easy to state but its inner working is rather mysterious. For example, until now even the number of steps of this bijection (viewed as an algorithm) remained wide open. In this talk I will discuss the geometry behind this bijection and state a number of complexity applications. Among other things, when the number of part sizes is bounded we show that the map of O'Hara's bijection can be computed in polynomial time, while O'Hara's algorithm is exponential. Needless to say, no previous knowledge of partition theory is assumed. This is joint work with Matjaž Konvalinka.