Abstract :
Let N(0, 2, n), respectively N(1, 2, n), denote the number of partitions of n whose ranks are even, respectively odd. We show here that N(0, 2, n) < N(1, 2, n), when n is even, and that this inequality is reversed, when n is odd. Our proof is ‘bijective’ in that we construct an injective map between the sets of partitions involved. We use a variation of the Involution Principle of Garsia and Milne.
