Restricted generalized Frobenius partitions (Q1100491)

In this paper generalized Frobenius partitions with certain restrictions on parts are studied. A generalized Frobenius partition of a positive integer n is a two-rowed array of non-negative integers \(\left( \begin{matrix} a_ 1...a_ r\\ b_ 1...b_ r\end{matrix} \right)\), where each row is arranged in non-increasing order and \(n=r+\sum^{r}_{i=1}(a_ i+b_ i).\) Andrews considered the enumerants for the Frobenius partitions of n in which the parts repeat at most k times and those in which parts are distinct and are colored with k colors. The author has studied the functions which enumerate Frobenius partitions of n in which each part is repeated at most h times and is colored with k given colors. Representations of the generating functions in terms of multidimensional theta functions and as sums of infinite products are obtained.