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arXiv · 1804.01651

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

Shane Chern·Shishuo Fu·Dazhao Tang
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Abstract

Motivated by Alladi's recent multi-dimensional generalization of Sylvester's 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 Cauchy's identity, and the product expressions of three classical theta functions studied by Gauss, Jacobi and Ramanujan.

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Shane Chern, Shishuo Fu, Dazhao Tang. 2018-04-05. Multi-dimensional $q$-summations and multi-colored partitions. https://arxiv.org/abs/1804.01651

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