Abstract

Two generalized partition theorems involving partitions with " n + 1 n + 1 copies of n n " and " n + 2 n + 2 copies of n n ", respectively, are proved. These theorems have potential of yielding infinite Rogers-Ramanujan type identities on MacMahon’s lines. Five particular cases are also discussed. Among them three are known and two provide new combinatorial interpretations of two known q q -identities.

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