Abstract
The number of partitions of a bi-partite number into at mostj parts is studied. We consider this function,p j (x, y), on the linex+y=2n. Forj≤4, we show that this function is maximized whenx=y. Forj>4 we provide an explicit formula forn j so that, for alln≥n j ,x=y yields a maximum forp j (x,y).
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Landman, B.M., Brown, E.A. & Portier, F.J. Partitions of bi-partite numbers into at mostj parts. Graphs and Combinatorics 8, 65–73 (1992). https://doi.org/10.1007/BF01271709
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DOI: https://doi.org/10.1007/BF01271709