Some inequalities for <Emphasis Type="Italic">k</Emphasis>-colored partition functions |
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| Authors: | Shane Chern Shishuo Fu Dazhao Tang |
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| Institution: | 1.Department of Mathematics,The Pennsylvania State University,University Park,USA;2.College of Mathematics and Statistics,Chongqing University,Chongqing,People’s Republic of China;3.College of Mathematics and Statistics,Chongqing University,Chongqing,People’s Republic of China |
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| Abstract: | Motivated by a partition inequality of Bessenrodt and Ono, we obtain analogous inequalities for k-colored partition functions \(p_{-k}(n)\) for all \(k\ge 2\). This enables us to extend the k-colored partition function multiplicatively to a function on k-colored partitions and characterize when it has a unique maximum. We conclude with one conjectural inequality that strengthens our results. |
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