Partitions of bi-partite numbers into at mostj parts |
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| Authors: | Bruce M. Landman Ezra A. Brown Frederick J. Portier |
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| Affiliation: | (1) Department of Mathematics, University of North Carolina at Greensboro, 27412 Greensboro, NC, USA;(2) Department of Mathematics, Virginia Tech, 24061 Blacksburg, VA;(3) Department of Mathematics, University of North Carolina at Greensboro, 27412 Greensboro, NC, USA |
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| Abstract: | The number of partitions of a bi-partite number into at mostj parts is studied. We consider this function,pj(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 fornj so that, for alln nj,x=y yields a maximum forpj(x,y). |
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