An Injection for the Ehrenpreis Rogers-Ramanujan Problem

摘要

Garsia and Milne used their elegant involution principle to give a bijective proof of the first Rogers-Ramanujan identity. We give an injection as called for by Ehrenpreis of the partitions of n into parts of the forms 5m + 2 and 5m + 3 into the partitions of n into parts of the forms 5m + 1 and 5m + 4. As observed by Ehrenpreis. Andrews and Baxter, this gives a potential start to a Rogers-Ramanujan bijection and a new partition identity involving partitions into parts >= 3 with difference between parts at least 2. Our potential bijection does not agree with the Garsia-Milne bijection.