Let G be an abelian group of order k. How is the problem of minimizing the number of sums from a sequence of given length in G related to the problem of minimizing the number of k-sums? In this paper we show that the minimum number of k-sums for a sequence a1, . . . , ar that does not have 0 as a k-sum is attained at the sequence b1, . . . , br−k+1,0, . . . ,0, where b1, . . . , br−k+1 is chosen to minimise the number of sums without 0 being a sum. Equivalently, to minimise the number of k-sums… CONTINUE READING