The first Göllnitz-Gordon identity states that the number of partitions of n in which the minimal difference between parts is at least 2, and at least 4 between even parts, equals the number of partitions of n into parts congruent to 1, 4, or 7 (mod 8). For example, taking n = 7, the resulting two sets of partitions are {(7), (6, 1), (5, 2)} and {(7), (4, 1, 1, 1), (1, 1, 1, 1, 1, 1, 1)}.

Andrews-Gordon identity | Göllnitz's theorem | Rogers-Ramanujan identities