A partition bijection related to the Rogers-Selberg identities and Gordon's theorem

We provide a bijective map from the partitions enumerated by the series side of the Rogers-Selberg mod 7 identities onto partitions associated with a special case of Basil Gordon's combinatorial generalization of the Rogers-Ramanujan identities. The implications of applying the same map to a special case of David Bressoud's even modulus analog of Gordon's theorem are also explored. Key words: partitions; Rogers-Ramanujan identities; Rogers-Selberg identities; Gordon's theorem; Andrews-Gordon-Bressoud theorem.

• Type: Journal
• Year: 2008
• Where: JCT
• Authors: Andrew V. Sills
• Keywords: Identities, JCT 2008, Rogers-Ramanujan Identities, Special Case