Some useful theorems for asymptotic formulas and their applications to skew plane partitions and cylindric partitions

Inspired by the works of Dewar, Murty and Kotěšovec, we establish some useful theorems for asymptotic formulas. As an application, we obtain asymptotic formulas for the numbers of skew plane partitions and cylindric partitions. We prove that the order of the asymptotic formula for the number of skew plane partitions of fixed width depends only on the width of the region, not on the profile (the skew zone) itself, while this is not true for cylindric partitions.