Vol. 10, No. 3, 2017

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ISSN: 1944-4184 (e-only)
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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
Milestones
Received: 14 March 2016
Accepted: 11 July 2016
Published: 14 December 2016

Communicated by Jim Haglund
Authors
Jacob Forster
Department of Mathematics, Statistics and Computer Science
St. Olaf College
Northfield, MN 55057
United States
Kristina Garrett
Department of Mathematics, Statistics and Computer Science
St. Olaf College
Northfield, MN 55057
United States
Luke Jacobsen
St. Olaf College
Northfield, MN 55057
United States
Adam Wood
Department of Mathematics, Statistics and Computer Science
St. Olaf College
Northfield, MN 55057
United States