PARITY RESULTS for PARTITIONS WHEREIN EACH PART APPEARS AN ODD NUMBER of TIMES

We consider the function f(n) that enumerates partitions of weight wherein each part appears an odd number of times. Chern ['Unlimited parity alternating partitions', Quaest. Math. (to appear)] noted that such partitions can be placed in one-to-one correspondence with the partitions of which he calls unlimited parity alternating partitions with smallest part odd. Our goal is to study the parity of in detail. In particular, we prove a characterisation of modulo 2 which implies that there are infinitely many Ramanujan-like congruences modulo 2 satisfied by the function The proof techniques are elementary and involve classical generating function dissection tools.