Partitions of bi-partite numbers into at most j parts

Bruce M. Landman; Ezra A. Brown; Frederick J. Portier

doi:10.1007/BF01271709

Partitions of bi-partite numbers into at most j parts

Bruce M. Landman, Ezra A. Brown, Frederick J. Portier

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

The number of partitions of a bi-partite number into at most j parts is studied. We consider this function, p_j(x, y), on the line x+y=2n. For j≤4, we show that this function is maximized when x=y. For j>4 we provide an explicit formula for n_j so that, for all n≥n_j, x=y yields a maximum for p_j(x,y).

Original language	English (US)
Pages (from-to)	65-73
Number of pages	9
Journal	Graphs and Combinatorics
Volume	8
Issue number	1
DOIs	https://doi.org/10.1007/BF01271709
State	Published - Mar 1992
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1007/BF01271709

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abstract = "The number of partitions of a bi-partite number into at most j parts is studied. We consider this function, pj(x, y), on the line x+y=2n. For j≤4, we show that this function is maximized when x=y. For j>4 we provide an explicit formula for nj so that, for all n≥nj, x=y yields a maximum for pj(x,y).",

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year = "1992",

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AU - Brown, Ezra A.

AU - Portier, Frederick J.

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AB - The number of partitions of a bi-partite number into at most j parts is studied. We consider this function, pj(x, y), on the line x+y=2n. For j≤4, we show that this function is maximized when x=y. For j>4 we provide an explicit formula for nj so that, for all n≥nj, x=y yields a maximum for pj(x,y).

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Partitions of bi-partite numbers into at most j parts

Abstract

ASJC Scopus subject areas

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