Abstract
In this second paper under the same title, some more weighted representations are obtained for various classical partition functions including p(n), the number of unrestricted partitions of n, Q(n), the number of partitions of n into distinct parts and the Rogers-Ramanujan partitions of n (of both types). The weights derived here are given either in terms of congruence conditions satisfied by the parts or in terms of chains of gaps between the parts. Some new connections between partitions of the Rogers-Ramanujan, Schur and Göllnitz-Gordon type are revealed.
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Dedicated to the memory of Professor Paul Erdős
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Alladi, K. (1998). Partition Identities Involving Gaps and Weights, II. In: Alladi, K., Elliott, P.D.T.A., Granville, A., Tenebaum, G. (eds) Analytic and Elementary Number Theory. Developments in Mathematics, vol 1. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-4507-8_3
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DOI: https://doi.org/10.1007/978-1-4757-4507-8_3
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