Generalizations and refinements of a partition theorem of Göllnitz.

One of the deepest results in the theory of partitions is a theorem of G llnitz [17]: Theorem G. Lei A(h) denote the number of partitions ofn intoparts = 2, 5, 1 1 (mod!2). Lei B(n) denote the number of partitions ofn into distinct parts = 2,4, 5 (modo). Lei C(h) denote the number of partitions ofn in the form ml + m2+ · · · +ms,no pari = l or 3, and such that mf — m£ + ± ^ 6 with strict inequality if mf = 6, 7 or 9 (mod 6). Then A(n) = B(n) = C(n). In Theorem G, and throughout, we adopt the convention that j = μ (mod M) means that j = μ + £M with j ^ μ and j > 0. The equality A (n) = B (n) is trivial because