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).
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics