Partitions of bipartite numbers |
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| Authors: | Jun Kyo Kim Sang Geun Hahn |
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| Institution: | (1) Department of Mathematics, Korea Advanced Institute of Science and Technology, 305-701 Taejon, Republic of Korea |
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| Abstract: | Letp
j(m, n) be the number of partitions of (m, n) into at mostj parts. We prove Landman et al.'s conjecture: for allj andn, p
j(x, 2n–x) is a maximum whenx-n. More generally we prove that for all positive integersm, n andj, p
j(n, m)=pj(m, n) pj(m–1, n+1) ifm n. |
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| Keywords: | 11P82 11P81 05A17 |
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