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On a Partition Theorem of Göllnitz and Quartic Transformations

✍ Scribed by Krishnaswami Alladi

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
336 KB
Volume
69
Category
Article
ISSN
0022-314X

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✦ Synopsis

For i=1, 2, 3, 4, let Q i (n) denote the number of partitions of n into distinct parts i (mod 4). New weighted identities in three free parameters are established connecting Q i (n) with partitions whose parts differ by 4 and such that consecutive members of the arithmetic progression #i (mod 4) cannot occur as parts. By the use of suitable quartic transformations, these weighted identities are shown to be reformulations of a deep partition theorem of Go llnitz. Applications include new relations for partitions of the Go llnitz-Gordon type, a new proof of Jacobi's triple product identity and a remarkable congruence modulo powers of 2 for Q 2 (n).

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