A Partition Theorem of Subbarao

Abstract

Let C(n) be the number of partitions of n such that all even multiplicities of the parts are less than 2m, m>1; and all odd multiplicities are at least (2r+1) and at most 2(m+r)—1, r≥0. Let D(n) be the number of partitions ofn into parts which are either odd multiples of (2r+1) or are even and not divisible by 2m.