Tree–Tree Matrices and Other Combinatorial Problems from Taxonomy

LetAbe a bipartite graph between two setsDandT.ThenAdefines, via Hamming distance, metrics on bothTandD.The question is studied which pairs of metric spaces can arise this way. If both spaces are trivial, the matrixAcomes from a Hadamard matrix or is a BIBD. The second question studied is howAcan be used to transfer (classification) information from one of the two sets to the other. These problems find their origin in mathematical taxonomy.