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math.CO2025
Some identities of the sums-of-tails type
Atul Dixit, Gaurav Kumar, Aviral Srivastava
A new sums-of-tails identity involving two parameters and is obtained and is used to derive more results of similar type. One of Ramanujan's sums-of-tails identities from t…
math.CO2025
Non-Rascoe partitions and a rank parity function associated to the Rogers-Ramanujan partitions
Atul Dixit, Gaurav Kumar, Aviral Srivastava
We study the generating function of the excess number of Rogers-Ramanujan partitions with odd rank over those with even rank, and, using combinatorial and analytical techniques, sh…