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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 |
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Vol. 10 (2017), No. 3, 523–530
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Abstract |
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We present a -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 -Delannoy numbers. |
Keywords
overpartitions, combinatorial proof, Delannoy numbers,
$q$-analogue
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Mathematical Subject Classification 2010
Primary: 05A17, 05A19
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Milestones
Received: 14 March 2016
Accepted: 11 July 2016
Published: 14 December 2016
Communicated by Jim Haglund
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Authors |
| Jacob Forster | |
| Department of Mathematics,
Statistics and Computer Science St. Olaf College Northfield, MN 55057 United States |
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| Kristina Garrett | |
| Department of Mathematics,
Statistics and Computer Science St. Olaf College Northfield, MN 55057 United States |
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| Luke Jacobsen | |
| St. Olaf College Northfield, MN 55057 United States |
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| Adam Wood | |
| Department of Mathematics,
Statistics and Computer Science St. Olaf College Northfield, MN 55057 United States |
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| © 2017 MSP (Mathematical Sciences Publishers). |
