Event Type:

Number Theory Seminar

Date/Time:

Tuesday, October 26, 2021 - 10:00 to 10:50

Location:

ALS 0006

Local Speaker:

Abstract:

In 1956, Alder conjectured that the number of d-distinct partitions of an integer n is always greater than or equal to the number of partitions of n into parts congruent to 1 or -1 modulo d+3. This conjecture generalized well known identities of Euler, Rogers and Ramanujan, and Schur. However, it was not until 2010 that Alderâ€™s Conjecture was proven to be true. In this talk, we overview the history and partial results from over those 60+ years. We also discuss a recent analogue of the Alder Conjecture which generalizes the second Rogers-Ramanujan identity. Finally, we discuss ongoing work with Holly Swisher to compute upper bounds on d-distinct partitions.

Host: