On restricted generalised Frobenius partitions
Padmavathamma · 1988
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 nonnegative integers (a1⋯arb1⋯br), where each row is arranged in nonincreasing order and n=r+∑ri=1(ai+bi). Andrews considered the enumerants for the Frobenius partitions of n in which the parts repeat at most k times and those in which the parts are distinct and are colored with k colors. The author has studied the functions which enumerate the 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.