A graphic construction of the collection formula for certain types of groups

Procedures for calculating P. Hall's famous collection formula for metabelian and two types of transmetabelian groups are described. Complicated combinatorial calculations are based on graphs corresponding to basic monomials. In conclusion programs written in PASCAL are given.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademiya Nauk SSSR, Vol. 191, pp. 140–151, 1991.