A note on the exact formulas for certain $2$-color partitions

Abstract

Let $p\le 23$ be a prime and $a_p(n)$ counts the number of partitions of $n$ where parts that are multiple of $p$ come up with $2$ colors. Using a result of Sussman, we derive the exact formula for $a_p(n)$ and obtain an asymptotic formula for $\log a_p(n)$. Our results partially extend the work of Mauth, who proved the asymptotic formula for $\log a_2(n)$ conjectured by Banerjee et al.

8 pages

References in corpus (1)

• A method of finding the asymptotics of q-series based on the convolution of generating functions