An Injection for the Ehrenpreis Rogers–Ramanujan Problem

✍ Scribed by Kevin W.J Kadell

• Book ID: 102584134
• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 79 KB
• Volume: 86
• Category: Article
• ISSN: 0097-3165
• DOI: 10.1006/jcta.1998.2929

✦ Synopsis

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.