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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.
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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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