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

14 years 12 days ago

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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.

Andrew V. Sills

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