Aequationes mathematicae - Tập 49 - Trang 86-97 - 1995
B. Richmond, A. Knopfmacher
The number of compositionsC(n) of a positive integern into distinct parts can be considered as a natural analogue of the numberq(n) of distinct partitions ofn. We obtain an asymptotic estimate forC(n) and in addition show that the sequence {C(n, k)} of distinct compositions ofn withk distinct parts is unimodal. Our analysis is more complicated than is usual for composition problems. The results im...... hiện toàn bộ
The so-called generalized associativity functional equation
$$\begin{aligned} G(J(x,y),z) = H(x,K(y,z)) \end{aligned}$$
has been investigated under various assumptions, for instance when the unknown functions G, H, J, and K are real, continuous, a...... hiện toàn bộ