Karl Mahlburg (MIT)

Asymptotics for partitions without sequences.

Partitions without sequences (i.e., containing no adjacent parts) were recently studied in connection to a wide variety of applications, including probability distributions and cellular automata. The main result of this talk is an asymptotic series expansion for the number of such partitions of size n. As shown by Andrews, the generating series for these partitions is the product of a theta function and one of Ramanujan's mock theta functions, and thus does not have the type of simple modular transformation properties that are typically used to make such estimates. In particular, any modular transformation introduces a non-holomorphic error integral, which are in fact part of the main term in the asymptotic expansion.