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On the asymptotics of certain colored partitions
Lukas Mauth
We will prove an infinite family of asymptotic formulas for the logarithm of certain two-colored partitions. An infinite sub-family of these asymptotics was posed as a conjecture b…
Exact formula for 1-lower run overpartitions
Lukas Mauth
We are going to show an exact formula for lower -run overpartitions. The generating function is of mixed mock-modular type with an overall weight We will apply an extended…
Log-concavity for partitions without sequences
Lukas Mauth
We prove log-concavity for the function counting partitions without sequences. We use an exact formula for a mixed-mock modular form of weight zero, explicit estimates on modified…
Exact formula for cubic partitions
Lukas Mauth
We obtain an exact formula for the cubic partition function and prove a conjecture by Banerjee, Paule, Radu and Zeng.