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arXiv 1908.086602019-08-23math.NT

An inequality between finite analogues of rank and crank moments

Pramod Eyyunni, Bibekananda Maji, Garima Sood

发表信息：: Int. J. Number Theory (Special issue in honor of Bruce C. Berndt), 2020
DOI：: 10.1142/S1793042120400217

英文摘要：

The inequality between rank and crank moments was conjectured and later proved by Garvan himself in 2011. Recently, Dixit and the authors introduced finite analogues of rank and crank moments for vector partitions while deriving a finite analogue of Andrews' famous identity for smallest parts function. In the same paper, they also conjectured an inequality between finite analogues of rank and crank moments, analogous to Garvan's conjecture. In the present paper, we give a proof of this conjecture.

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