In this paper, we introduce Partition theory and 1974 CONJECTURE 1 OF ANDREWS on two three-parameter partition functions Al, k, a(n)and Bl, k, a(n). Conjecture 1 for k = a+1 and show that it is false for k ≥ a+2. Further, we explain an introduction of Schur's 1926 theorem on partitions. We also introduce 1974 CONJECTURE 2 OF ANDREWS on partitions. Further, we state Bressound’s conjecture, which states that two sets of partitions under certain constraints are equinumerous. The validity of the conjecture in the first two cases implies exactly the partition-theoretical interpretation for the Rogers-Ramanujan identities.