摘要
This paper studies a special form of integer partition of . n, where the target is to find a . maximal partition . P, with the maximum number of parts, that does not include any partition of . f as its subset. Let . ρ(f,n) denote the number of parts in~. P. We show that such a problem is closely related to the . tiny-pan coin weighing problem where each pan of the balance scale can hold exactly one coin, thereby deriving exact bounds for . ρ(f,n) in some of the cases. Furthermore, we show that . ρ(f,n) is ultimately periodic as a function of . n, so that the computation of . ρ(f,n), and its corresponding maximal partition, can be sped up.