Karl Mahlburg (MIT)<BR><BR>


Asymptotics for partitions without sequences. <BR><BR>


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.