I am familiar with the partition function p(k,n) where p is the number of partitions of n using only natural numbers at least as large as k. Is there a way of determining if p(k1, n1) > p(k2, n2) that does not actually use the partition function? To clarify, I want to know if there is a quick way to tell if the number of partitions of k1, n1 is greater than or less than the number of partitions of k2, n2 without using the partition function.

Thanks!

--Connor