# Seminar: May 18, 2009

## Igor Pak, University of Minnesota

## Combinatorics and Complexity of Partition Bijections

The study of partition identities has a long history going back to Euler, with applications ranging from Analysis to Number Theory, from Enumerative Combinatorics to Probability. Partition bijections is a combinatorial approach which often gives the shortest and the most elegant proofs of these identities. These bijections are then often used to generalize the identities, find "hidden symmetries", etc. In the talk I will present a modern approach to partition bijections based on the complexity ideas and geometry of random partitions. We show that certain "natural" bijections do not exist, even for some classical partition identities.