The celebrated Rogers–Ramanujan identities are a pair of combinatorial identities stating that the number of integer partitions of n ( \(n\in {\mathbb {N}}_0\) ) with parts congruent to \(\pm 1 \pmod {5}\) (respectively \(\pm 2 \pmod {5}\) ) equals the number of partitions of n with super-distinct parts (respectively super-distinct parts with no 1s). In this paper, we consider related combinatorial moment functions, and establish bias results, generalizing both the Rogers–Ramanujan identities and results of Ballantine and the author. We also interpret these results in terms of k-marked partitions, and pose related open problems of interest.
