ABSTRACT
For example, P = (8, 5, 3, 2, 1, 1, 1) is Ramsey for the pair 8, 13. Table 3.1 in Section 3.2 lists the other 45 Ramsey partitions for the pair 8, 13. Recall further that the algorithm then calls for one player to cut the cake in pieces whose sizes are in the ratios P1 : P2 · · · : Pn and the non-cutter to circle the pieces he or she would judge to be at least as large as the cutter thinks them to be. If we call these circled pieces "acceptable" (to the non-cutter), then, because the partition is Ramsey, either the non-cutter can get his or her fair share from acceptable pieces or the cutter can get his or her fair share from unacceptable pieces. In the latter case, the non-cutter is giving away a portion of the cake that is considered smaller than the cutter's share. In both cases, the cutter receives pieces that total exactly the cutter's share. In either case, fair division in the ratio a : b is easily accomplished.
