New Weighted Rogers-ramanujan Partition Theorems and Their Implications

@inproceedings{BERKOVICH2000NewWR,
  title={New Weighted Rogers-ramanujan Partition Theorems and Their Implications},
  author={KRISHNASWAMI ALLADI AND ALEXANDER BERKOVICH},
  year={2000}
}
  • KRISHNASWAMI ALLADI AND ALEXANDER BERKOVICH
  • Published 2000
This paper has a two-fold purpose. First, by considering a reformulation of a deep theorem of Göllnitz, we obtain a new weighted partition identity involving the Rogers-Ramanujan partitions, namely, partitions into parts differing by at least two. Consequences of this include Jacobi’s celebrated triple product identity for theta functions, Sylvester’s famous refinement of Euler’s theorem, as well as certain weighted partition identities. Next, by studying partitions with prescribed bounds on… CONTINUE READING

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