Albert Nijenhuis

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The Frobenius problem, also known as the postage-stamp problem or the money-changing problem, is an integer programming problem that seeks nonnegative integer solutions to x 1 a 1 + · · · + x n a n = M , where a i and M are positive integers. In particular, the Frobenius number f (A), where A = {a i }, is the largest M so that this equation fails to have a(More)
If p(n, k) is the number of partitions of n into parts <k. then the sequence { p(k, li), p(k + 1, Ii)....} is periodic modulo a prime p. We find the minimum period Q = Q(li, p) of this sequence. More generally, we find the minimum period, modulo the number of partitions of n whose parts all lie in a fixed finite set T of positive integers. We find the(More)
In this note we describe a general principle for selecting at random from a collection of combinatorial objects, where " at random " means in such a way that each of the objects has equal probability, a priori, of being selected. We apply this principle by displaying two algorithms, the first of which will select a random partition of an integer n, and the(More)