Multi-dimensional $q$-summations and multi-colored partitions
Combinatorics
2018-04-06 v1
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.
Cite
@article{arxiv.1804.01651,
title = {Multi-dimensional $q$-summations and multi-colored partitions},
author = {Shane Chern and Shishuo Fu and Dazhao Tang},
journal= {arXiv preprint arXiv:1804.01651},
year = {2018}
}
Comments
9 pages, 2 figures