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

• Autores: George E. Andrews
• Localización: Inventiones mathematicae, ISSN 0020-9910, Vol. 169, Nº. 1, 2007, págs. 37-73
• Idioma: inglés
• DOI: 10.1007/s00222-007-0043-4
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• Resumen

  • 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.