A variation on a theme of Sylvester — a smoother road to Göllnitzʹs (Big) theorem Original Research Article

Using graphical representation, a simple bijective proof of the following result is given: ‘The number of partitions of a positive integer n into distinct odd parts equals the number of partitions of n into parts ≠ 2 and differing by ⩾ 6, where the inequality is strict if a part is even’. A three-parameter refinement of this result is obtained and shown to be equivalent to a deep partition theorem of Göllnitz.