An Upper Bound for the General Restricted Partition Problem
W. J. A. Colman · The Fibonacci Quarterly · 1987
The function p*(p19 p29 ••• » pm I ri) is defined as the number of partitions of the integer n into at most m positive integers p19 p2,..., p, • where the order is irrelevant. An upper bound for the number of partitions is given. This upper bound is then compared with two known particular cases. An upper bound for the function p*(pl9 p 2,..., pm;^n) is also given. This last function represents the number of partitions of all integers between 0 and n into at most m positive integers p., * p? ,..., p. 1.