Constructing a Higher-Dimensional Inheritance State from Tiled Quartet States
(A) Initially, the inheritance states of each quartet pair are independently labeled. Considering the pedigree shown, at some particular position of the reference genome individuals B, C, and D have all received identical alleles from the two parents, and so are genetically identical. Individual A received distinct alleles from both parents and so is nonidentical with respect to each of the other three. The binary representations of each quartet state are inconsistent when placed in register with respect to each other.
(B) After enumerating all arbitrary reassignments of the first two indicators, the best consistent matching of all six indicators produces a consensus binary representation of the sextet inheritance state. At this position, the first two indicators of each of the B and C, B and D, and C and D quartets are flipped, requiring that the second two indicators in each quartet also be flipped in order to maintain the consistency of the inheritance state.