Ramanujan’s Partial Theta Series and Parity in Partitions
نویسنده
چکیده
A partial theta series identity from Ramanujan’s lost notebook has a connection with some parity problems in partitions studied by Andrews in [3], where 15 open problems are listed. In this paper, the partial theta series identity of Ramanujan is revisited and answers to Questions 9 and 10 of Andrews are provided.
منابع مشابه
Ramanujan's lost notebook: Combinatorial proofs of identities associated with Heine's transformation or partial theta functions
Combinatorial proofs are given for certain entries in Ramanujan’s lost notebook. Bijections of Sylvester, Franklin, and Wright, and applications of Algorithm Z of Zeilberger are employed. A new bijection, involving the new concept of the parity sequence of a partition, is used to prove one of Ramanujan’s fascinating identities for a partial theta function.
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