On the collection process for positive words

We present an approach to studying the divisibility of the exponents of the commutators that arise in collection formulas obtained for positive words of a free group. It deals with logical formulas that establish a connection between the exponents of the commutators and the structure of the positive word to which the collection process is applied. Using our approach, we obtain several generalizations of known collection formulas with some divisibility properties of the exponents.