Alexandru Ciolan
Published 2018-06-02Version 1
In this paper we prove that the number of partitions into squares with an even number of parts is asymptotically equal to that of partitions into squares with an odd number of parts. We further show that, for $ n $ large enough, the two quantities are different and which of the two is bigger depends on the parity of $ n. $ This answers a recent conjecture formulated by Bringmann and Mahlburg (2012).
Congruences for the difference of even and odd number of parts of the cubic and some analogous partition functions
Asymptotics of the number of partitions into p-cores and some trigonometric sums
Two congruences involving Andrews-Paule's broken 3-diamond partitions and 5-diamond partitions
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