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A Partition Bijection Related To The Rogers-Selberg Identities And Gordon's Theorem, Andrew Sills

Department of Mathematical Sciences Faculty Publications

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.