A fragment-cofragment model of antibody incidence structures

In the predecessor to this paper, "Uncovering Antibody Incidence Structures," Markowsky and Wohlgemuth presented a model which allowed one to calculate best possible solutions for the relation between individuals and antibodies given certain sets of tests each of which is analyzed simply for the presence or absence of a reaction. In this paper, we show that many of the concepts and theorems of the first paper generalize to the case where we actually try to compare the strengths of various reaction tests. As one might expect, the resulting model has a greater ability to detect the presence of antibodies than the model presented in the first paper. Furthermore, the additional information generated by the model described in this paper allows one to present a fairly concise definition of the best possible solution for a given amount of reaction test data.