An injection for the Ehrenpreis Rogers-Ramanujan problem (Q1291128)

The author gives an injection from the partitions of an integer \(n\) into parts of the form \(5m+2\) and \(5m+3\) into the partitions of \(n\) into parts of the form \(5m+1\) and \(5m+4\). The problem to determine such an injection was raised by Ehrenpreis and is connected to the Roger-Ramanujan identities. The injection could possibly be usefull for creating a bijection needed in a bijection proof for those identities. The bijection found by Garsia and Milne in their bijective proof of the first Rogers-Ramanujan identity is different from the one that possibly could be obtained from the present injection.