A Partition Bijection Related to the Rogers-Selberg Identities and Gordon\u27s Theorem

We provide a bijective map from the partitions enumerated by the series side of the Rogers–Selberg mod 7 identities onto partitions associated with a special case of Basil Gordon\u27s combinatorial generalization of the Rogers–Ramanujan identities. The implications of applying the same map to a special case of David Bressoud\u27s even modulus analog of Gordon\u27s theorem are also explored