Negative Quartet Estimates by Embedding of Triplet and Quintet Invariants

Negative quartet invariants play an important role in direct procedures: they can be actively used in the phasing process or, in a passive way, for selecting the correct solution in multisolution approaches. Unfortunately their average reliability is small. The use of the second representation of the quartets may lead to improved estimates but calculations are expected to be too extensive even for modem computers. The simple and fast process described in this paper provides improved quartet estimates by embedding triplet and quintet estimates. The first applications of the method are satisfactory.