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Partitions, Durfee symbols, and the Atkin–Garvan moments of ranks

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Abstract

Atkin and Garvan introduced the moments of ranks of partitions in their work connecting ranks and cranks. Here we consider a combinatorial interpretation of these moments. This requires the introduction of a new representation for partitions, the Durfee symbol, and subsequent refinements. This in turn leads us to a variety of new congruences for our ‘marked’ Durfee symbols much in the spirit of Dyson’s original conjectures on the ranks of partitions.

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Authors and Affiliations

  1. Pennsylvania State University, University Park, PA, 16802, USA

    George E. Andrews

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  1. George E. Andrews
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Correspondence to George E. Andrews.

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Mathematics Subject Classification (2000)

05A17, 05A19, 11P83

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Andrews, G. Partitions, Durfee symbols, and the Atkin–Garvan moments of ranks. Invent. math. 169, 37–73 (2007). https://doi.org/10.1007/s00222-007-0043-4

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  • DOI: https://doi.org/10.1007/s00222-007-0043-4

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