The number of genotypic assignments on a genealogy. I. The method and simple examples

This paper demonstrates how the number of possible genotypic assignments consistent with the rules of Mendelian genetics and with any known phenotypes can be calculated for an arbitrary genealogy. This is of interest both in the contest of the uses of the Metropolis algorithm for pedigree analysis and in its own right. Bounds on the number of states for certain regular and random genealogies are also obtained, and further results will be given in a later paper.