Tree-Tree Matrices and Other Combinatorial Problems from Taxonomy

Let A be a bipartite graph between two sets D and T. Then A defines by Hamming distance, metrics on both T and D. The question is studied which pairs of metric spaces can arise this way. If both spaces are trivial the matrix A comes from a Hadamard matrix or is a BIBD. The second question studied is in what ways A can be used to transfer (classification) information from one of the two sets to the other. These problems find their origin in mathematical taxonomy. Mathematics subject classification 1991: 05B20, 05B25, 05C05, 54E35, 62H30, 68T10