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arXiv · 1102.1814

Inequalities for full rank differences of 2-marked Durfee symbols

Kathrin Bringmann·Ben Kane
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Abstract

In this paper, we obtain infinitely many non-trivial identities and inequalities between full rank differences for 2-marked Durfee symbols, a generalization of partitions introduced by Andrews. A certain strict inequality, which almost always holds, shows that identities for Dyson's rank, similar to those proven by Atkin and Swinnerton-Dyer, are quite rare. By showing an analogous strict inequality, we show that such non-trivial identities are also rare for the full rank, but on the other hand we obtain an infinite family of non-trivial identities, contrasting the partition theoretic case.

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Kathrin Bringmann, Ben Kane. 2011-09-27. Inequalities for full rank differences of 2-marked Durfee symbols. https://arxiv.org/abs/1102.1814

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