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Multi-dimensional $q$-summations and multi-colored partitions

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 نشر من قبل Tang Dazhao
 تاريخ النشر 2018
  مجال البحث
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Motivated by Alladis recent multi-dimensional generalization of Sylvesters classical identity, we provide a simple combinatorial proof of an overpartition analogue, which contains extra parameters tracking the numbers of overlined parts of different colors. This new identity encompasses a handful of classical results as special cases, such as Cauchys identity, and the product expressions of three classical theta functions studied by Gauss, Jacobi and Ramanujan.



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