Threshold arrangements and the knapsack problem

We show that a combinatorial question which has been studied in connection with lower bounds for the knapsack problem by V.E. Brimkov and S.S. Dantchev [An alternative to Ben-Or’s lower bound for the knapsack problem complexity, Applied Mathematics Letters 15 (2) (2002) 187–191] is related to threshold graphs, threshold arrangements, and other well-studied combinatorial objects, and we correct an error in the analysis given in that paper.