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math.CO2014
An overpartition analogue of the -binomial coefficients
Jehanne Dousse, Byungchan Kim
We define an overpartition analogue of Gaussian polynomials (also known as -binomial coefficients) as a generating function for the number of overpartitions fitting inside the $…
math.NT2014
Asymptotic formulae for partition ranks
Jehanne Dousse, Michael H. Mertens
Using an extension of Wright's version of the circle method, we obtain asymptotic formulae for partition ranks similar to formulae for partition cranks which where conjectured by F…
math.CO2014
A generalisation of a partition theorem of Andrews to overpartitions
Jehanne Dousse
In 1969, Andrews proved a theorem on partitions with difference conditions which generalises Schur's celebrated partition identity. In this paper, we generalise Andrews' theorem to…