Sylvie Corteel

S. Corteel, CNRS, LRI, Université Paris Sud, Orsay

Overpartitions and basic hypergeometric series

Overpartitions were introduced by Corteel and Lovejoy in 2001 to understand
the combinatorics behind Ramanujan's 1psi1 summation. But their history goes
way back as their generating function is the inverse of a theta function. Indeed
the Hardy-Ramanujan collaboration started by ``Ramanujan's false statement''
that the coefficient of qn is 1/θ4(q), which is the number of overpartitions of n,
is the nearest integer to

                                                                                       

In this talk, I will show that overpartitions are the good tool to understand the
combinatorics of basic hypergeometric series. I will also show that numerous
results on partitions are special cases of results of overpartitions. I will illustrate
this idea by presenting Rogers-Ramanujan type results on overpartitions.