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A variation on a theme of Sylvester — a smoother road to Göllnitz's (Big) theorem

✍ Scribed by Krishnaswami Alladi

Book ID: 104114182
Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 698 KB
Volume: 196
Category: Article
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(98)00193-9

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✦ Synopsis

Using graphical representation, a simple bijective proof of the following result is given: 'The number of partitions of a positive integer n into distinct odd parts equals the number of partitions of n into parts # 2 and differing by > 6, where the inequality is strict if a part is even'. A threeparameter refinement of this result is obtained and shown to be equivalent to a deep partition theorem of Giillnitz.

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