On the coefficients in the associative expansion of a Lie word (Q1176028)

Using the results of their preceding papers on the topic [Note Mat. 8, No. 1, 111-121 (1988; Zbl 0715.17005) and Suppl. Rend. Circ. Mat. Palermo, II. Ser. 23, 201-208 (1990; see the following review)] the authors find non-trivial relations between the coefficients in the expansion of a left normed Lie monomial in some variables as the sum of associative monomials in the same variables. The main problem is the cycle decomposition of the permutations of the variables in the associative monomials thus arising. The authors succeed in finding the sum of the coefficients of all monomials whose associated permutations belong to a given conjugacy class.