Karl Mahlburg

Affiliation: MIT

Email: mahlburg@math.mit.edu

Title Of Talk: Asymptotics for partitions without sequences

Abstract: 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 modular transformation properties that are typically used to make such estimates. In particular, the non-holomorphic error integrals that appear in the transformations are in fact part of the main term of the asymptotic expansion.

Last update made Fri Feb 15 17:39:28 EST 2008.
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