Classification of greedy subset-sum-distinct-sequences Original Research Article

We consider subset-sum-distinct-sequences having the property that no subset sum is congruent to a mod q for any given integers a and q. We provide a classification of these sequences, in order to determine which of the sequences have maximal reciprocal sums. A greedy sequence is one which tries to maximize its reciprocal sum by making each successive term in the sequence as small as possible. We describe the circumstances under which a greedy sequence does in fact have maximal reciprocal sum. In classifying the greedy sequences, we resolve two of the three conjectures made in J. Baeʹs paper of 1998, An extremal problem for subset-sum-distinct sequences with congruence conditions (Discrete Math. 189 (1998) 1–20).