1 A ug 2 00 3 A Four - parameter Partition Identity

where Par denotes the set of all partitions, |λ| denotes the size (sum of the parts) of λ, θ(λ) denotes the number of odd parts in the partition λ, and θ(λ) denotes the number of odd parts in the conjugate of λ. A combinatorial proof of Andrews’ result was found by Sills in [2]. In this paper, we generalize this result and provide a combinatorial proof of our generalization. This gives a simpler combinatorial proof of (1) than the one found in [2].