Partitions with Non-Repeating Odd Parts and Q-Hypergeometric Identities

Krishnaswami Alladi ()
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Krishnaswami Alladi: University of Florida, Department of Mathematics

A chapter in The Legacy of Alladi Ramakrishnan in the Mathematical Sciences, 2010, pp 169-182 from Springer

Abstract: Summary We obtain a series expansion for the product generating function of partitions in which the odd parts do not repeat. This is done by studying the 2-modular Ferrers graphs of such partitions via Durfee squares. This provides a unified approach to several fundamental identities in the theory of partitions and q-series such as those of Sylvester, Lebesgue, Gauss, and Rogers-Fine, and provides links with Göllnitz’s deep theorem.

Keywords: Partitions; Non-repeating odd parts; 2-modular Ferrers graphs; q-series (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4419-6263-8_9

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DOI: 10.1007/978-1-4419-6263-8_9

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