Vol. 10, No. 3, 2017

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A bijective proof of a $q$-analogue of the sum of cubes using overpartitions

Jacob Forster, Kristina Garrett, Luke Jacobsen and Adam Wood

Vol. 10 (2017), No. 3, 523–530
Abstract

We present a $q$-analogue of the sum of cubes, give an interpretation in terms of overpartitions, and provide a combinatorial proof. In addition, we note a connection between a generating function for overpartitions and the $q$-Delannoy numbers.

Keywords
overpartitions, combinatorial proof, Delannoy numbers, $q$-analogue
Mathematical Subject Classification 2010
Primary: 05A17, 05A19