Dendrogram topology: capacity and retrieval

摘要

This paper defines the 'capacity' of dichotomous dendrograms of a given order as the total number of topologically different cases. By using a combinatorial approach based on the number of possible cases for each part of a root dichotomy and extending this through the dendrogram, the capacity for each order may be calculated. By saving a 'principal divisions table' accumulated during the calculation of the capacity, sufficient information is retained for a recursive search through the table that will generate a 'D-array' uniquely describing the topology of any specified dendrogram. This search procedure is called 'dendrogram retrieval.' Of general interest will be the large capacity (e.g. about 1011) for even quite low (e.g. D35) orders of dendrogram.