Partition bijections

Igor Pak
University of California, Los Angeles (UCLA)

The study of partition identities goes back to the works of Euler, Gauss and Jacobi, and have been flourishing ever since. In the late 19th century, J.J. Sylvester singlehandedly revolutionized the field by introducing a "constructive approach" of proving partition identities with partition bijection, and showing how to apply it in a number of important cases. As we understand now, the highly positive outlook on the power of partition bijections was destroyed by Ramanujan who introduced literally hundreds of new partitions identities, many of which were (and some still are) difficult to prove even analytically. In this lecture I will give a broad survey of partition bijection proving various pre- and post-Ramanujan partition identities. At the end I will also hint at what went wrong.

Presentation (PDF File)

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