Open Access
2017 A bijective proof of a $q$-analogue of the sum of cubes using overpartitions
Jacob Forster, Kristina Garrett, Luke Jacobsen, Adam Wood
Involve 10(3): 523-530 (2017). DOI: 10.2140/involve.2017.10.523

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.

Citation

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Jacob Forster. Kristina Garrett. Luke Jacobsen. Adam Wood. "A bijective proof of a $q$-analogue of the sum of cubes using overpartitions." Involve 10 (3) 523 - 530, 2017. https://doi.org/10.2140/involve.2017.10.523

Information

Received: 14 March 2016; Accepted: 11 July 2016; Published: 2017
First available in Project Euclid: 12 December 2017

zbMATH: 1351.05035
MathSciNet: MR3583880
Digital Object Identifier: 10.2140/involve.2017.10.523

Subjects:
Primary: 05A17 , 05A19

Keywords: $q$-analogue , combinatorial proof , Delannoy numbers , overpartitions

Rights: Copyright © 2017 Mathematical Sciences Publishers

Vol.10 • No. 3 • 2017
MSP
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